Reference no: EM131051440
Analytical methods for engineers(calculus) tasks 1,2 and 3
Assignment brief
Scenario
The design and development department associated with a power generation plant has various issues Mich require resolving, you are now asked to provide an analysis of these issues with respect to the questions detailed below:
Task 1:
a. Differentiate the following using product rule
(i) y = xlnx (ii) y = x3sin 2x
b. Differentiate the following using quotient rule
(i) y = x/1-x (ii) y = 3ln5t/cos2t
c. Differentiate the following using function of a function rule
(i) y = 2/√(x2 - 3x + 5) (ii) y = 4 tan34x
d. Differentiate y = x3ln3x/exsin2x - with respect to x
Task 2
a. If y = 3x4 + 2x3 - 3x + 2
find
(i) dy/dx (ii) d2y/dx2 (iii) d3y/dx3
b. Find dy/dx and d2y/dx2 when y = ln(x2 -1)
c. Find dy/dx and d2y/dx2 when y = sin-16x
d. Find dy/dx and d2y/dx2 when y = tanh-14x
Task 3
Determine the following integrals
(a) ∫xsinx dx using integration by parts
(b) ∫2et/√(et + 4)dt using integration by substitution
(c) ∫4x-3/(x + 1)2dt using integration by partial fractions
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