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115 results.

Shaheen's copy of Functions of two variables: Locate stationary point
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Question in WM175_A1_24 by Shaheen Charlwood and 1 other

Find the stationary point $(p,q)$ of the function: $f(x,y)=ax^2+bxy+cy^2+dx+gy$ . Calculate $f(p,q)$ .
CF Maths In class test two mock paper question 4
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Question in Deactivated user's workspace by Jinhua Mathias

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$ . Find stationary points, local and global maxima and minima of $g$ on $I$
CF Maths January test mock paper finding stationary points
Ready to use
Question in Deactivated user's workspace by Jinhua Mathias

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$ . Find stationary points, local and global maxima and minima of $g$ on $I$
Ugur's copy of Maclaurin series (three terms)
Ready to use
Question in Ugur's workspace by Ugur Efem and 1 other

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$ .
Ugur's copy of Taylor series (three terms)
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Question in Ugur's workspace by Ugur Efem and 1 other

Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$ .
DIfferentiation: product rule
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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 $f^{\prime}(x)= (a + b x)^{m-1} e ^ {n x}g(x)$ .
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 $f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$ .
Sine and Cosine Functions
Draft
Question in DIAGNOSYS by Christian Lawson-Perfect and 3 others

No description given
Sine and Cosine
Draft
Question in DIAGNOSYS by Christian Lawson-Perfect and 3 others

No description given
Julie's copy of Second order differential equations 2
Draft
Question in Julie's workspace by Julie Crowley

Method of undermined coefficients:

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$ . (Equal roots example). Includes an interactive plot.

rebelmaths
Julie's copy of Second order differential equations 1
Draft
Question in Julie's workspace by Julie Crowley

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$ .

rebelmaths
Graphs: Horizontal scale transformation
Ready to use
Question in Graphing and Polynomials by Ben Brawn

of a random cubic spline
Graphs: Vertical shift transformation
Ready to use
Question in Graphing and Polynomials by Ben Brawn

of a random cubic spline
Graphs: Two random transformations
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Question in Graphing and Polynomials by Ben Brawn

Horizontal and vertical shifts and scales of a random cubic spline
Graphs: Three random transformations
Ready to use
Question in Graphing and Polynomials by Ben Brawn

Horizontal and vertical shifts and scales of a random cubic spline
Graphing: Four random transformations
Ready to use
Question in Graphing and Polynomials by Ben Brawn

Horizontal and vertical shifts and scales of a random cubic spline
Graphs: Vertical scale transformation
Ready to use
Question in Graphing and Polynomials by Ben Brawn

of a random cubic spline
Graphs: Horizontal shift transformation
Ready to use
Question in Graphing and Polynomials by Ben Brawn

of a random cubic spline
Graphs: Random Single Transformation
Ready to use
Question in Graphing and Polynomials by Ben Brawn

Horizontal and vertical shifts and scales of a random cubic spline
Chain rule - product of two functions
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$ . Find $g(x)$ .
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 $\arcsin$ .
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 $\displaystyle \int\frac{ax+b}{(1-x^2)^{1/2}} \;dx$ . Solution involves inverse trigonometric functions.
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$ .
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.
Hyperbolic Functions 4
Draft
Question in Bill's workspace by Bill Foster

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$
Hyperbolic Functions 3
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$
Hyperbolic Functions 1
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $a\cosh(x)+b\sinh(x)=c$ . There are two solutions for this example.
Hyperbolic Functions 2
Draft
Question in Bill's workspace by Bill Foster

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$
Product rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate $(a+bx) ^ {m} \sin(nx)$

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