Calculus Answers

Differentiate f(x) = 5𝑥³+7𝑥 2𝑥²−4𝑥+5 using quotient rule. 

f(x) = 2x⁴ + 8x³ - 16x² - 96x + 100

f'(x)=?

Question:

If 𝑎 and 𝑏 are two sides of a right angled hypotenuse 𝑐 and let 𝑝 be the perpendicular from the opposite

vertex on the hypotenuse, show that:

1. (𝛿 𝑝/𝛿𝑎)_b =b³/c³

2. (𝛿𝑝/𝛿𝑎 )_A=b/c

Find the directional derivative of (x,y,z) = xsin yz at (1,3,0) in the direction of i+2j-k

The position of a particle is given by r(t)= t²i + e^2tj + In(t+1)k. Find the minimum velocity of the particle

If curl F=0, F is said not to be

A firms short run production function is given by Q=c * L + B * L^2 - a * L^3

at a=17.6, b=84.9 and c=73

determine the value of L which maximises the average product of labour rounding your answer to two (2) decimal places

Which of the following values represent the definite integral "\\displaystyle{\\int_{0}^{\\pi\/4}e^{\\tan{\\theta}}\\sec^2{\\theta}d\\theta}"

1) "e ^2"

2) e - 1

3) e/2

4) e

Which of the following represents the integral "{\\int \\frac{1}{x\\ln{x}}dx}"

1) "ln(lnx)+C"

2) "ln(xlnx)+C"

3) "lnxlnx+C"

4) None of the above