Mathematics

Find $\frac{f(a+h)-f(a)}{h}$ and simplify where. f(x) = 6x - 9

Find $\frac{f(a+h)-f(a)}{h}$ and simplify where. f(x) = sin x

Find $\frac{f(a+h)-f(a)}{h}$ and simplify where. f(x) = x³ + 2x² - 1

A stone falls from a height of 60 m on the ground, the height h after x second is approximately given by h(x) = 40 - 10x² (i) What is the height of the stone when (a) x = 1 sec? (b) x = 1.5 sec? (c) x = 1.7 sec? (ii) When does the stone strike the ground?

Show that the parametric equations: x = at² , y = 2at represent the equation of parabola y² = 4ax

Show that the parametric equations: x = a cosθ , y = b sin θ represent the equation of ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Prove the identities: sinh 2x = 2 sinh x cosh x

Prove the identities: sech² x = 1 - tanh² x

Prove the identities: csch² x = coth² x - 1

Determine whether the given function f is even or odd. f(x) = x³ + x

Determine whether the given function f is even or odd. f(x) = (x + 2)²

Determine whether the given function f is even or odd. $f(x)=x\sqrt{x^2+5}$

Determine whether the given function f is even or odd. $f(x)=\frac{x-1}{x+1},x\ne -1$

Determine whether the given function f is even or odd. $f(x)=x^{\frac{2}{3}}+6$

Determine whether the given function f is even or odd. $f(x)=\frac{x^3-x}{x^2+1}$

Find the domain and the range of the function g defined below , and sketch of graph of g . $g(x)=\frac{x^2-16}{x-4}$

Let $f(x)=\sqrt{x^2-9}$ . Find the domain and range of f.

Let $f(x)=\frac{x}{x^2-4}$ . Find the domain and range of f.

Determine whether the following functions are even or odd . $f(x)=3x^4-2x^2+7$

Determine whether the following functions are even or odd . $f(x)=\frac{3x}{x^2+1}$