Calculus Answers

Study the following functions

3) f(x) = (x³ / x-1 )s

4) f(x) = x / cube root of (x²-1)

Study the following functions

1)f(x) = Inx/x

2) f(x) = e^x-x +3

Find the general solution of these differential equations.

1) dy/dx = x/y² 2)dy/dx = x+2 / y

5) ʃ (1-sinx /1-cosx)e^x dx

6) ʃ₀^π/4 cosθ +isinθ / 2cos²θ dθ

Evaluate the following Integrals

3)  ʃ_-1¹ (x + 1/2) √(x²+x+1)dx

4)  ʃ (x+2) / √(x+3) dx

Evaluate the following Integrals

1)  ʃ [2x² / (x-1)²(x+1)] dx

2)  ʃ [2x³-3x²-x-7 / 2x²-3x-2] dx

Find f'(x) iff(x) = e^x(1+Inx)

f(x) = x³e^1/x

f(x) = √[x²-1](x+1) / (x²+1)^3/2

Find f'(x) if

f(x)= √[In(e^2x + e^-2x)]

f(x) = e^-2x sin2x

Evaluate the limit as x turns to 3

Lim √(x+1) - 2 / x-3