# Category:Mathematical exercise

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## Subcategories

This category has only the following subcategory.

### S

- Solution to mathematical exercise (22 pgs)

## Pages in category "Mathematical exercise"

The following 200 pages are in this category, out of 525 total.

(previous page) (next page)### A

- Achilles and the tortoise/Series/Exercise
- Alternating geometric series/R/Modulus z below 1/Exercise
- Alternating series/Leibniz criterion/Coffee in student flat/Change of strategy/Exercise
- Alternating series/Leibniz criterion/Coffee in student flat/Exercise
- Arc-sine/Arc-cosine/Derivative/Exercise
- Area/Below sine graph/Exercise
- Area/Between Parabola and -2x^2+3x+4/Exercise
- Arithmetic and geometric mean/Estimate/Exercise
- Attention curve/-x^2+25x-100/Optimum of 8 to 18/Exercise

### B

- Base change/123/471/025 and 024/661/35-2/Point with coordinates 254/General/Exercise
- Base change/7-4/81 and 46/73/Point with coordinates -25/General/Exercise
- Base change/Standard basis in R^4/Example/Exercise
- Base change/Transformation matrix/C/Standard basis and 3+5i 1-i/2+3i 4+i/Exercise
- Base change/Transformation matrix/R^4/Standard basis and permutated standard basis/Exercise
- Base change/Transformation matrix/Standard basis and 451/23-8/57-3/Exercise
- Bernoulli inequality/Exponent is 3/Where wrong/Exercise
- Binomial coefficient/Incidence formula/Exercise
- Binomial coefficient/Natural number/Exercise
- Binomial coefficient/Sum in Pascal triangle/Fact/Proof/Exercise
- Binomial coefficient/Sum/Exercise

### C

- Chain rule/R/x^2+5x-2 over x+1 and y-2 over y^2+3/Confirm/Exercise
- Chain rule/R/x^3+4x^2-1 and y^2-y+2/Confirm/Exercise
- Clock/6/Hands/Opposition/Exercise
- Clock/Minute- and second hand/Angle formula/Exercise
- Compact interval/Monotone function/Riemann-integrable/Exercise
- Compact interval/Real function/Riemann integrable on subdivision/Fact/Proof/Exercise
- Complex and real partial fraction decomposition/1 over x^4-1/Exercise
- Complex Conjugation/Rules/Fact/Proof/Exercise
- Complex Multiplication/Real Determinant/Exercise
- Complex numbers/(1+i)^n/n up to 5/Exercise
- Complex numbers/Computation of square root/Explicite for b negative/Exercise
- Complex numbers/Computations/Exercise
- Complex numbers/Conjugation real part modulus/Fact/Proof/Exercise
- Complex numbers/Field/Fact/Proof/Exercise
- Complex numbers/Inverse element/Via real system/Exercise
- Complex numbers/Multiplication/Real matrix/Exercise
- Complex numbers/Quadratic equation has solution/Exercise
- Complex numbers/Real and imaginary part/Properties/Fact/Proof/Exercise
- Complex numbers/Roots of x^3-1/Exercise
- Complex numbers/Rules for modulus/Exercise
- Complex numbers/Square root of i/etc/Exercise
- Complex numbers/z^2+5iz-3 is 0/Solve/Exercise
- Complex partial fraction decomposition/1 over x(x-1)(x-2)(x-3)/Exercise
- Complex partial fraction decomposition/1 over x^2(x^2+1)/Exercise
- Complex partial fraction decomposition/1 over x^3(x-1)^3/Exercise
- Complex partial fraction decomposition/1 over x^3-1/Exercise
- Complex partial fraction decomposition/x^3+4x^2+7 over x^2-x-2/Exercise
- Complex vector space/Finite dimensional/Real Basis/Exercise
- Complexe Numbers/Real and Imaginary part/Conjugation/Linearity/Exercise
- Composition/Continuous function followed by staircase function/No staircase function/Exercise
- Composition/Polynomial example/1/Exercise
- Composition/Staircase function followed by function/Staircase function/Exercise
- Cone/Linear form/Coprime/Exercise
- Cone/Two-dimensional/Edges/Signature/Exercise
- Connectedness of Cities/Exercise
- Continuous function/Between too local maxima/Minimum/Exercise
- Continuous function/Bonded on bounded intervall/No maximum/Example/Exercise
- Continuous function/Closed interval to itself/Fix point/Exercise
- Continuous function/Closed interval to onesided open/Not surjective/Exercise
- Continuous function/Closed interval/Continuous Continuation/Exercise
- Continuous function/Integral equality/Point equality/Exercise
- Continuous Function/Q to R/Finitely many values/Not constant/Exercise
- Continuous Function/R to R/Finitely many values/Constant/Exercise
- Continuous function/x sin 1 over x/On 0,1/Infinitely many zeroes/Exercise
- Continuous Funktion/Sum of even and odd function/Exercise
- Continuous real function/Positive/Positive in neighborhood/Exercise
- Convergent series in 0 1/Riemann-integrable function/Series of integrals to a n/Exercise
- Curve study/(2x+3) e to the power -x^2/Exercise
- Curve study/e to the power -1 over x/Exercise
- Curve study/e^(-2x)-2e^(-x)/x not negative/Morse potential/Exercise
- C^2/(2+7i,3-i) and (15+26i,13-7i)/Linearly independent/Exercise
- C^2/(2-7i,-3+2i) and (5+6i,3-17i)/Linearly independent/Exercise

### D

- Definite integral/2x^3+3e^x-sin x/-1 to 0/Exercise
- Definite integral/Computation/x sin x^2/Exercise
- Definite integral/Computation/x^2+3x-6 over x-1/From 2 to 5/Exercise
- Definite integral/Computation/x^3-2x^2-x+5 over x+1/From 1 to 7/Exercise
- Definite integral/Estimate for modulus/Exercise
- Definite integral/e^(t^2)/From 0 to x/Equals 1/Exercise
- Definite integral/From 1 over n+1 to 1 over n/Exercise
- Definite integral/sqrt(x) - 1 over sqrt(x) +1 over (2x+3)-e^(-x)/1 to 4/Exercise
- Derivation/Extension to localization/Exercise
- Derivation/Lie-bracket/Multiplication/Exercise
- Derivative/(g(f(x)))^2f(g(x))/f is x^2-1 and g is x+2/Exercise
- Derivative/Direct/x^3+2x^2-5x+3/Exercise
- Derivative/R/Product of n functions/Exercise
- Determinant and volume/Area/Parallelogram/Exercise
- Determinant/3x3/Multilinarity/Direct/Exercise
- Determinant/3x3/Permutation matrices/Exercise
- Determinant/4x4/Exercise
- Determinant/C/Compute/1+3i 5-i/3-2i 4+i/Exercise
- Determinant/C/Compute/1+i 3-2i 5/i 1 3-i/2i -4-i 2+i/Exercise
- Determinant/Compute/1 3 5/2 1 3/8 7 4/Exercise
- Determinant/Diagonal block matrix/Left lower block 0/Exercise
- Determinant/Elementary matrices/Exercise
- Determinant/Expansion for arbitrary row or column/Exercise
- Determinant/Inverting algorithm on general matrix/Exercise
- Determinant/Multiplication/2x2/Example/Exercise
- Determinant/Multiplication/3x3/Example/Exercise
- Determinant/Recursive/Upper triangular matrix/Diagonal product/Exercise
- Determinant/Several expansions/027/145/603/Exercise
- Differentiable functions/Larger and derivative larger/Exercise
- Differential equation/Inhomogeneous linear/Separable variables/y' is ty+t/Exercise
- Differential equation/Separable variables/y' is 1 over sin y/Exercise
- Differential equation/Separable variables/y' is exp y/Exercise
- Differential equation/Separable variables/y' is ty/Exercise
- Differential equation/Separable variables/y' is ty^2 over t^2-1/Exercise
- Differential equation/Separable variables/y' is ty^2/Exercise
- Differential equation/Separable variables/y' is t^3y^3/Exercise
- Differential equation/Separable variables/y' is y/Exercise
- Differential equation/y' is y/Exercise
- Differential equations/Solutions/1 over y and +-ty^3/Confirm via derivatives/Exercise
- Differential operator/Algebraic/Inductive and product condition/Fact/Proof/Exercise
- Disk/C/N points/Exist point with distance above n/Exercise
- Division with remainder (polynomials)/C/(5+i)x^4+ix^2+(3-2i)x-1/x^2+ix+3-i/Exercise
- Division with remainder (polynomials)/Q/3x^4+7x^2-2x+5/2x^2+3x-1/Exercise

### E

- Elementary matrices/Invertible/Explicite/Exercise
- Elementary matrices/Multiplication from right/Action/Exercise
- Elementary row operations/Column rang constant/Exercise
- Euler's number/Computation with exponential series/4 digits/Exercise
- Exponential function/Linear function as tangent/Exercise
- Exponential series/K/Estimate for remainder/Exercise
- Exponential series/R/Estimate for remainder/Exercise

### F

- Factorial function/Continuity/Exercise
- Factorial function/Fac (x) equals integral 0 to 1 (-ln t)^x/Exercise
- Factorial function/Increasing/10! geq e^(11)/Estimate with exponential function/Exercise
- Factorial function/Recursive formula for 2k-1/Exercise
- Family of vectors/Scaling/Generating system and linearly independent/Exercise
- Family/Age/Linear system/Exercise
- Fibonacci-numbers/Binet formula/Exercise
- Fibonacci-numbers/Fraction/Convergence and limit/Exercise
- Fibonacci-numbers/Simpson formula/Exercise
- Field extension/Q in R/Basis/Exercise
- Field/2 elements/Linear system/Exercise
- Field/Basic properties/Rules for sign/Fact/Proof/Exercise
- Field/General distributivity law/Exercise
- Field/Rules for fractions/Exercise
- Field/Uniqueness of inverse element/Fact/Proof/Exercise
- Finite geometric series/Real/Exercise
- Flat function/Polynomial in 1 over x times exp -1 over x/Derivative/Exercise
- Flat function/Polynomial in 1 over x times exp -1 over x/Limit for x to 0/Exercise
- Free fall/Constant gravitation/No air resistance/Exercise
- Function limit/b^c/b to 0/c positive/Exercise
- Function limit/Several fractions/Exercise
- Function limit/Sine 1 over x/Several factors/Exercise
- Function/1+ln x -1 over x/Bijection/Exercise
- Function/Finitely many values/No staircase function/Exercise
- Function/Piecewisely defined/1/Continuity/Exercise
- Function/R/Taking powers/Injective and surjective/Exercise
- Function/t^x e^(-t)/Maximum in t/Exercise
- Function/x^2+x-1/0 and 1/Zero/Interval bisection/Exercise
- Function/x^3-3x+1/0 and 1/Zero/Interval bisection/Exercise
- Functions/R/Strongly increasing/Injective/Exercise

### G

- G-adic numbers/Convergence/Exercise
- Geometric series/2 over 3/Third member/Exercise
- Geometric series/Another beer/Exercise
- Geometric series/Compute for 1 over 5/Exercise
- Geometric series/Exponential series/Cauchy product/Fifth member/Exercise
- Geometric series/R/Even and odd indices/Exercise
- Growth of population/Logistic differential equation/Example/Properties of solution curves/Exercise

### H

- Harmonic series/Even and uneven subseries/Divergence/Exercise
- Heron's method/Square root of 5/Four members/Start value 2/Exercise
- Homogeneous polynomial/Representation with formal partial derivatives/Exercise
- Homothety/Composition/Multiplication of determinant/Exercise
- Homothety/Determinant/Exercise
- Hyperbolic cosine/Monotonicity behavior/Exercise
- Hyperbolic cosine/R/Power series/Odd Coefficients 0/Exercise
- Hyperbolic functions/R/Derivatives/Exercise
- Hyperbolic functions/R/Elementary properties/Fact/Proof/Exercise
- Hyperbolic sine/Increasing/Exercise
- Hyperbolicus tangent/R/Image/Exercise

### I

- Implicite function theorem/Recall/Exercise
- Improper integral/1 over (x+1) sqrt(x)/0 to infty/Exercise
- Improper integral/1 over sqrt(1-t^2)/-1 to 1/Computation/Exercise
- Improper integral/Both sides/Monotoneous approximation of endpoints/Exercise
- Improper integral/Bounded interval/Continuous extension/Existence/Exercise
- Improper integral/Continuous unbounded positive function/Improper integral exists/Example/Exercise
- Improper integral/e^(-t)/0 to infty/Exercise
- Improper integral/Independence of starting point/Exercise
- Improper integral/sin x over x/0 to infty/Exercise
- Improper integral/x^2-3x+5 over x^4+2x^3+5x+8/1 to infty/Exercise
- Improper integral/x^3-3x+5 over x^4+2x^3+5x+8/0 to infty/Exercise
- Increasing function/R to R/Sequence limit and function limit/Exercise
- Induction/2m+1 Product (2i-1)^2/Product 4k^2-1/Exercise
- Induction/3^n \geq n^4/Exercise
- Induction/6^(n+2)+7^(2n+1) divisible by 43/Exercise
- Induction/Alternating sum of squares/Exercise
- Induction/Partition of chocolate/Exercise
- Inflation/2 percent/Doubling/Exercise
- Initial value problem/y' is y times t over t^2+2/y(3) is 7/Exercise
- Integral/Dependence on parameter/at^2-a^2t/-1 to 2/Extrema/Exercise
- Integral/Root 3x^2+5x-4/Exercise
- Intermediate value theorem/Not for Q/Exercise
- Intersection of planes/3x+4y+5z is 2 and 2x-y+3z is -1/Line equation/Exercise
- Interval/-4 to 5/6 subintervals/Staircase integral/Exercise
- Inverse function/Power series approach/sin x/0/Degree 4/Exercise
- Invertible matrix/Find inverse matrix/123/6-1-2/037/Exercise
- Invertible matrix/Find inverse matrix/232/504/1-23/Exercise
- Invertible matrix/Find inverse matrix/27/-49/Exercise
- Invertible matrix/Find inverse matrix/C/2+3i 1-i/5-4i 6-2i/Exercise