Calculus Answers

What are the sum rule, the product rule, and the quotient rule. 2 examples

ACTIVITY IN BASIC CALCULUS

QUOTIENT RULE

  I. Find the derivative of the following functions below using the quotient rule. Show your complete solution.

1. "\\frac{x^2-7x}{2x^3+5x^2}"
2. "\\frac{3x^2+7x-14}{x^3-4x^2}"
3. "\\frac{2x^3+8x^2}{x^2+6x^2-10}"

II. Create your own given problem involving quotient rule and solve. Show your complete solution. Do not copy the given example below.

1. Example must have two different terms in numerator, and three different terms in denominator

eg. (do not copy)

y= "\\frac{8x^2-3x}{x^2+6x^2-10}"

2. Example must have three different terms in numerator, and three different terms in denominator

eg. (do not copy)

y= "\\frac{x^2+8x^2-3x}{2x^3+6x^2-10}"

Determine the dimensions of the right circular cylinder of

greatest volume that can be inscribed in a right circular cone of

radius 6 cm and height 9 cm.

Find the first partial derivative of

f(x,y) = "(4x-y)\/(4x+y)" at the point (4,2) for both x and y.

5. Decompose

(i)

x2 +x +1

(x +3)(x2 −x +1)

(ii)

x4 −x3 −2x2 +4x +1

x (x −1)2

3. Find a polynomial, P(x), of degree 3 with zeros of 4,1 and −1, if P(0) = 8.

2. Let P (x) = 2x4 +15x3 +31x2 +20x +4

(a) Determine whether (x −1) is a factor of P (x). (2)

(b) Find all the possible rational zeros of P (x) by using the Rational Zeros Theorem. (2)

(c) Solve P (x) = 0

Find the moment about the x-axis of a wire of constant density that lies along The curve

𝑦 = √𝑥 from 𝑥 = 0 𝑡𝑜 𝑥 = 2

Find the Center of mass of a thin plate of constant density 𝛿 covering the region bounded by the parabola 𝑦 = 𝑥² and the line 𝑦 = 4.

Two Children balance on the seesaw. The 40 lb child is 5 ft from the fulcrum. How far from the fulcrum is the 50 lb child ?