(PDF) Engineering Mathematics

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Added on 2020-10-22

(PDF) Engineering Mathematics

Added on 2020-10-22

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Table of ContentsQuestion 1:.......................................................................................................................................3Find the following equations.......................................................................................................3Question 2:.......................................................................................................................................4Differentiate................................................................................................................................4Question 3: ......................................................................................................................................5The energy E stored in a spring is given by the formula E = 200 x ^ 2 where x is thecompression. The rate of change of the energy with respect to the compression is called thethrust T of the spring...................................................................................................................5Question 4:.......................................................................................................................................6Find dy/ dx at the point (0, 2) given that y ^ 3 = 8 + xe^ y ........................................................6Question 5. ......................................................................................................................................6The total force due to a distributed load acting on a beam from x = a to x = b is given by........6∫a-b f(x)dx....................................................................................................................................6Question 6:.......................................................................................................................................8Evaluate the following integrals using integration by parts:.......................................................8

Question 1:Find the following equations(a) limx→−5 (25 – x^2 / x^2 + 2 x- 15)Ans: => 25-x ^ 2 / x^2 + 2 x-15= - x-5 / x-3= 25- x^2 / x^2 + 2 x -15Factors: -x^2 + 25 : (x+5)(x-5)= - (x+5)(x-5) / x^2 + 2 x - 15Factor x ^ 2 + 2 x – 15=-(x+5)(x-5) / (x-3)(x+5)cancel the common factor : x+5= - x-5/ x-3= lim x->-5 (-x-5 / x-3)Putting value x= -5= – -5-5 / -5-3= - 10 / 8cancel common factor:= -5/4(b) limx→∞ 4x^2 – 19 / 3x^2 + 11Ans: limx→∞ (4 x^2-19 / 3 x^2+11)Divide by highest denominator power:4- 19/x^2 / 3+ 11/x^2= limx→∞ (4 - 19/x^2 / 3+ 11/x^2)= limx→∞ (4 - 19/x^2) / limx→∞ (3+ 11/x^2)= limx→∞ (4 – 19/x^2) = 4 : simplify = limx→∞ (3+ 11/x^2) = 3 : simplify= 4 / 3

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(PDF) Engineering Mathematics