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31 results.

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 $f^{\prime}(x)= (a + b x)^{m-1} e ^ {n x}g(x)$ .
Solving exponential equations using logs
Ready to use
Question in Algebra by Ben Brawn

No description given
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
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
Logarithms: Solving equations 5
Ready to use
Question in Bill's workspace by Bill Foster

Given $\rho(t)=\rho_0e^{kt}$ , and values for $\rho(t)$ for $t=t_1$ and a value for $\rho_0$ , find $k$ . (Two examples).
BS3.6
Draft
Question in Bill's workspace by Bill Foster

Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised.
Logarithms: Solving equations 3
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $\log(ax+b)-\log(cx+d)=s$
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

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

Differentiate $\sin(ax+b) e ^ {nx}$ .
Product rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate the function $(a + b x)^m e ^ {n x}$ using the product rule.
Product Rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate the function $f(x)=(a + b x)^m e ^ {n x}$ using the product rule. Find $g(x)$ such that $f\;'(x)= (a + b x)^{m-1} e ^ {n x}g(x)$ .
Interactive Newton-Raphson method
Should not be used
Question in Christian's workspace by Christian Lawson-Perfect and 1 other

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$ . If $x_0=1$ find $x_1$ .

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.
Unbiased estimator for exponential distribution
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Arrivals given by exponential distribution, parameter $\theta$ and $Y$ , sample mean on inter-arrival times. Find and calculate unbiased estimator for $\theta$ .
Integration: Indefinite integral
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$ .
Integration by parts
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$ , find $g(x)$ . Find $h(x)$ , $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$ .
Definite integration using standard integrals
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Calculate definite integrals: $\int_0^\infty\;e^{-ax}\,dx$ , $\int_1^2\;\frac{1}{x^{b}}\,dx$ , $\; \int_0^{\pi}\;\cos\left(\frac{x}{2n}\right)\,dx$
Indefinite integration using standard integrals
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Integrate $f(x) = ae ^ {bx} + c\sin(dx) + px^q$ . Must input $C$ as the constant of integration.
Integration By Parts
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Integrating by parts.

Find $\int ax\sin(bx+c)\;dx$ or $\int ax e^{bx+c}\;dx$
Find CDF of given exponential distribution, and expectation and variance,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given the PDF for $Y \sim \operatorname{Exp}(\lambda)$ find the CDF, $P(a \le Y \le b)$ and $\operatorname{E}[Y],\;\operatorname{Var}(Y)$
Calculate probabilities using the exponential distribution,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Calculating simple probabilities using the exponential distribution.
Differentiation: Product rule
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate $\sin(ax+b) e ^ {nx}$ .
Differentiate product of binomial and exponential
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate the function $(a + b x)^m e ^ {n x}$ using the product rule.
Differentation: Product Rule
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate the function $f(x)=(a + b x)^m e ^ {n x}$ using the product rule. Find $g(x)$ such that $f\;'(x)= (a + b x)^{m-1} e ^ {n x}g(x)$ .
Second order ODE with constant coefficients and boundary conditions
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$ .
Solve a second order ODE with repeated roots,
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$ . (Equal roots example).
Solving log equations using exponentials
Ready to use
Question in Algebra by Ben Brawn

No description given
Interactive Newton-Raphson method
Ready to use
Question in Bill's workspace by Bill Foster

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$ . If $x_0=1$ find $x_1$ .

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.
Julie's copy of Indefinite integral
Draft
Question in Julie's workspace by Julie Crowley

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$ .
Phil's copy of Integration by parts, Exponential 20/10
Ready to use
Question in Phil's workspace by Phil Barker

Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$ , find $g(x)$ . Find $h(x)$ , $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$ .
Integration by parts, Exponential 31/10
Ready to use
Question in Katie's workspace by Katie Dexter

Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$ , find $g(x)$ . Find $h(x)$ , $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$ .

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