Calculus Answers

If the demand function is P = 70 - Q find an expression for TR in terms of Q.

(1) Differentiate TR with respect to Q to find a general expression for MR in terms of Q. Hence write

down the exact value of MR at Q = 60.

(2) Calculate the value of TR when

(a) Q=60 

(b) Q=61

and hence confirm that the 1 unit increase approach gives a reasonable approximation to the exact value of MR obtained in part (1).

Find an equation of the tangent line to the curve 𝑦 = 2𝑥 2 + 3 that is parallel to the line 8𝑥 – 𝑦 + 3 = 0

Find the derivative using chain rule-d/dx: 

5.y = (4x - 9) * (3x - 4) ^ 2

6.y = x/(x ^ 2 - 2) ^ 2)

7.) y =(x²-7)²(2x - 5)³

8. y = (x ^ 4 - 2x) ^ 2/(x - 1) ^ 3

9. y = sqrt(x - 2) ^ 2

10.) y = (x ^ 3 + x ^ 2) ^ 2 * (x - 1) ^ 3

Water is being poured at the rate of 2π cubic meter/min into an inverted conical tank that is 12-meter deep with a radius of 6 meters at the top. If the water level is rising at the rate of 1/6 m/min and there is a leak at the bottom of the tank, how fast is the water leaking when the water is 6-meter deep?

find the area of the surface generated when the given arc is revolved about the y axis ( y= 4 - x^2 from x=0 to x=2 )

Find the surface area of that part of the plane 4𝑥+5𝑦+𝑧=8

4x+5y+z=8 that lies inside the elliptic cylinder (x²/100) + (y²/81) =1

Given that y= acoskx + bsinkx, show that d²y/dx² + k²y =0

ACTIVITY IN BASIC CALCULUS

BASIC RULES IN DERIVATIVE

 Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.

1. f(x) = -₄x⁵+ ______x^-4 - 2468

2. f (x) =____x^-3- _____x^1/4 - 12x

3.f(x)= ____ "\\sqrt[4]{x^3} - \\underset{x^6}{=} + \\frac{2}{3} x^6"

4.f (x) = "\\underset{x^-6}{=} -" ____ x² + "\\sqrt[4]{x}"