MAT 120 (lab) Solved

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Problem Sheet 5

Calculus: Limit, Derivative, Integration and Taylor’s series
1. Find out the following limit:
sin x x3 4x15 x3 5x
i) limx0 x ii) limx3 x3 iii) limx 2×3 3×2
2. Find out the first, second and third derivatives of following functions with respect to x i) xx
ii) 5×5 4×4 9×3 16×2 7x2
5 3.  2 y3 sinxy = ? x 
4. Work out the following indefinite integrals
i) sin(axb)dx ii) (ln x) dx
5. Evaluate the following definite integrals
a /2
i) exdx ii) sin xdx
0 0
6. Work out the Taylor series of the following functions about x/2, up to order x/28 i) lnx ii) sin x
Optimization: Relative maxima and minima
7. Find the relative minimum and relative maximum of the following function:
f (x)  x3 30x


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