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2730 questions · page 115 of 137 · choose a topic above to narrow them down

SA-FP-RA-G012 marksL2 StandardNon-calculatorReduction formulae

I_n=\int_0^1x^ne^xdx

with

I_n=e-nI_{n-1}

and

I_0=e-1

. Find

I_1

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SA-FP-RAT-0023 marksL2 StandardNon-calculatorAsymptotes

Find the oblique asymptote of

y=\dfrac{x^2+3x+4}{x+1}

, giving

y

in terms of

x

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SA-FP-RAT-0042 marksL2 StandardNon-calculatorAsymptotes

Find the

x

-values of the vertical asymptotes of

y=\dfrac{x^2-4}{x^2-1}

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SA-FP-ROOT-0012 marksL2 StandardNon-calculatorSymmetric functions

For the same equation

x^2-5x+3=0

, find

\dfrac1\alpha+\dfrac1\beta

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SA-FP-ROOT-0033 marksL2 StandardNon-calculatorSymmetric functions

x^3+2x^2-x+3=0

has roots

\alpha,\beta,\gamma

. Find

\alpha^2+\beta^2+\gamma^2

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SA-FP-ROOT-0043 marksL2 StandardNon-calculatorTransformed roots

x^2-5x+3=0

has roots

\alpha,\beta

. The equation

y^2+py+q=0

has roots

2\alpha

and

2\beta

. Find

q

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SA-FP-ROOT-G012 marksL2 StandardNon-calculatorSymmetric functions

x^2-5x+3=0

has roots

\alpha

and

\beta

. Find

\alpha^2+\beta^2

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SA-FP-RR-0022 marksL2 StandardNon-calculatorFirst order

Find the constant solution

u_n=k

u_{n+1}=2u_n+3

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SA-FP-RR-0032 marksL2 StandardNon-calculatorSecond order

Find the roots of the auxiliary equation for

u_{n+2}=5u_{n+1}-6u_n

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SA-FP-SUM-0022 marksL2 StandardNon-calculatorStandard sums

Find

\displaystyle\sum_{r=11}^{20}r

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SA-FP-SUM-0032 marksL2 StandardNon-calculatorDifferences

Using

\dfrac1{r(r+1)}=\dfrac1r-\dfrac1{r+1}

, find

\displaystyle\sum_{r=1}^{9}\dfrac1{r(r+1)}

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SA-FP-SUM-0041 markL2 StandardNon-calculatorDifferences

State the sum to infinity of

\displaystyle\sum_{r=1}^{\infty}\dfrac1{r(r+1)}

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SA-FP-TL-0012 marksL2 StandardNon-calculatorLimits

Find

\displaystyle\lim_{x\to0}\frac{1-\cos x}{x^2}

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SA-FP-TL-0032 marksL2 StandardCalculatorTaylor series

Find the coefficient of

(x-2)^2

in the Taylor series of

e^x

about

x=2

(to 4 s.f.).

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SA-FP-VD-0012 marksL2 StandardNon-calculatorPoint distances

Find the distance from

(1,1,1)

to the plane

x+2y+2z=14

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SA-FP-VD-0022 marksL2 StandardNon-calculatorTriple product

Find the volume of the parallelepiped with edges

\begin{pmatrix}1\\0\\0\end{pmatrix}

\begin{pmatrix}0\\2\\0\end{pmatrix}

\begin{pmatrix}1\\1\\3\end{pmatrix}

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SA-FP-VD-0042 marksL2 StandardNon-calculatorPoint distances

Find the distance from

(2,3,4)

to the

x

-axis.

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SA-FP-VI-0012 marksL2 StandardNon-calculatorImproper integrals

Evaluate

\displaystyle\int_1^\infty\frac{dx}{x^2}

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SA-FP-VI-0022 marksL2 StandardNon-calculatorImproper integrals

Evaluate

\displaystyle\int_0^1\frac{dx}{\sqrt x}

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SA-FP-VI-0032 marksL2 StandardNon-calculatorMean value

Find the mean value of

x^2

over

0\le x\le3

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