Calculus Answers

Sketch the graph of the function f defined by f(x) =x⁴+8x³, clearly giving all the properties used in it.

Evaluate integral x⁴/(1+x²)⁴ dx from 0 to ∞ using a reduction formula for the product of trigonometric
functions.

Integral d/dx(x² - x⁴/a²)

Find the fourier series of f(x) of the given interval: f(x)= 1/2 x belongs to (-1,0)
-1/2 x belongs to (0,1)
Is the function above even or odd?

Please help differentiate this:

The height of a certain species 't' years after it was planted is given by
H=20ln(3t +2) +30cm
a) how tall was the shrub when it was planted
b) how long will it take for the shrub to reach a height of 1 metre
c)At what rate is the shrubs height changing
i) 3 years after being planted
ii) 10 years after being planted

How do I prove this statement using properties of numbers: If a < 0, b < 0, then √ab ≤ −(a+b)/2?

Find the slope of tangent to the curve y= √ (3x-8) at the point where x = 11

Limit as x approaches 0+ (x^2/2) – (1/x)

find numbers a,b, and k so that f is continuous
F(x) { x^2, if x<=9 and kx, if x>9

use intermediate value theorem to prove x(x-3)^2=3 has a solution between 2 and 4