Math Answers

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

find limit x approaches -2+ (x+3) [(|x+2|) / (x+2)]

limit as t →∞(4t^2-8)/(t-2)

for what value of k, is the function f, defined by,
f(x)={[sin(1+x)-sin(1-x)]/x, when x≠0 ; kcos1, when x=0
continuous at x=0?

find out for which value of k the function f, given by
f(x)={ (1-cos4x)/x^2 , when x≠0 ; k(2+sin^(2) x), when x=0
is continuous at x=0.