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131 results.

CF Maths In class test three question 8 Integration by partial fractions with limits
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Question in Deactivated user's workspace by Jinhua Mathias

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d$ .
DIfferentiation: product rule
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Differentiate the function $f(x)=(a + b x)^m e ^ {n x}$ using the product rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1} e ^ {n x}g(x)$ .
Factorise a quadratic
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 2 others

Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors.
Integration: Indefinite integral by substitution
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$
Equation of a straight line
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$ .
Differentiation: quotient rule
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$ .
Demo of automatically generating unresolved matrix product output
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Question in Linear Algebra 1st year by Julia Goedecke

Matrix multiplication. Contains a function that will let you print the calculation steps of matrix multiplication, e.g. in the Advice.
Chain rule - trig and quadratic
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 2 others

Differentiate $\displaystyle \cos(e^{ax}+bx^2+c)$
Chain rule - binomial
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Differentiate $\displaystyle (ax^m+b)^{n}$ .
Chain rule - square root of polynomial
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Differentiate

$\sqrt{a x^m+b})$
Chain rule - log of binomial
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate $\displaystyle \ln((ax+b)^{m})$
Integration by partial fractions
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Question in Bill's workspace by Bill Foster and 1 other

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.
Numbas demo: video
Ready to use
Question in Demos by Christian Lawson-Perfect

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.
Solving equations
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $\log_{a}(x+b)- \log_{a}(x+c)=d$
Solving equations
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$ .

Make sure that your choice is a solution by substituting back into the equation.
Quotient rule. (Video)
Draft
Question in Bill's workspace by Bill Foster

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$ . Find $g(x)$ .

Contains a video solving a similar quotient rule example. Although does not explicitly find $g(x)$ as asked in the question, but this is obvious.
Logarithms: Solving equations 2
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$ .

Make sure that your choice is a solution by substituting back into the equation.
Logarithms: Solving equations 1
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $\log_{a}(x+b)- \log_{a}(x+c)=d$
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int\frac{ax+b}{(1-x^2)^{1/2}} \;dx$ . Solution involves inverse trigonometric functions.
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \frac{c}{\sqrt{a-bx^2}}\;dx$ . Solution involves the inverse trigonometric function $\arcsin$ .
Leicester: Integration 3
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx$ and hence find $\displaystyle \int (ax+b)^2\sin(cx+d)\; dx$

Also two other questions on integrating by parts.
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$ .
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$ .
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

Find the polynomial $g(x)$ such that $\displaystyle \int \frac{ax+b}{(cx+d)^{n}} dx=\frac{g(x)}{(cx+d)^{n-1}}+C$ .
Hyperbolic Functions 4
Draft
Question in Bill's workspace by Bill Foster

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$
Solving equations
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $\displaystyle ax ^ 2 + bx + c=0$ .

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