Calculus Answers

x=cos

3

t,y=sin

3

t,t∈[0,2π]

x=cos3⁡t,y=sin3⁡t,t∈[0,2π]

1. Using the chain rule differentiate the following function.

a. y=(2x2+4x-2)2

b. y=(x2+2x-4)2

2. Using the product rule differentiate the following functions.

a. y=2x2-x2(1/2x2+5)2

b. y=(x+2)2(x+3)2

3. Using the quotient rule differentiate the following functions.

a. y=x2/(3x+5)2

b. y=e2x/x2+2

4. Differentiate the following functions.

a. y=x2e2x

b. y=ln(x+2x+1)

5. Differentiate the following functions (with respect of to x).

a. fx=2x2+3x(4x2-2)

b. fx=ln2x2+3e2+x

6. Differentiate the following functions and find the value of x.

a. y=x2+3x(x-2)

b. y=x2-3/x+2

Thank You

Let f be differentiable on R. Suppose f'(x) not equal 0 for every x. Prove that f has at most one real root

Continue the two sequences of numbers below and find an equation to each of the sequences: n 1 2 3 4 5 6 7 Equation an 2 5 9 14 20 27 bn 1 3 12 60 360 2520

Please tell the complete solution of this question.

Let {a_n} be an arithmetic sequence such that its 1^st, 20^th, and 58^th terms are consecutive terms of some geometric sequence. Find the common ratio of the geometric sequence.

Question:

A particle moves such that its vector is given by 𝑟

 = cos 𝜔𝑡𝑖 + sin 𝜔𝑡𝑗 where 𝜔 is a constant. Show that:

(i)

Velocity, 𝑣 of the particle is perpendicular to r

(ii)

Acceleration, 𝑎 is directed towards the origin and has magnitude proportional to the 

distance from the origin

(iii) 𝑟 𝑋 𝑣is a constant vector