Reference no: EM13333919
Question 1.
Find the following limits:
Question 2.
Differentiate
(a) esin(x2);
(b) ln sin-1x3, where sin-1 x is an inverse function for sin x, i.e. sin-1x = arcsin x.
Question 3.
The energy E stored in a spring is given by the formula E = 100x2 where x is the compression. The rate of change of the energy with respect to the compression is called the thrust T of the spring.
(a) Express the thrust T of the spring in terms of x,
(b) Find the energy E at x = 1:5,
(c) Find the thrust T at x = 1:5,
(d) Find the compression x when the energy E = 500,
(e) Find the compression x when the thrust T = 100.
Question 4.
Find dy/dx at the point (0, 8) given that y = 8 + xey
Question 5.
(a) Find the indefinite integral of f(x) = 6x-2x3 - x√x + 3ex.
(b) Hence calculate 0∫1 (6x-2x3-x√x + 3ex) dx.
Question 6.
Evaluate the following integrals using integration by parts:
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