4th Quarter Basic Calculus

1. A function f(x) is continuous when all of the following are satisfied except

• limit of f(x) exists

• f(x) is defined

• f(x) is removable

• limit of F(x) = f(a)

 $\ What\ is\ the\ derivative\ of\ x^4+3x^3+1$  

•  $4x^3+9x^2+1$  

•  $4x^2+9x$  

•  $4x^3+9x^2$  

•  $4x^2+9x$  

 $Find\ the\ derivative\ of\ x^{4\ }+3x^3-5x$  

•  $4x^3+9x^2-5$  

•  $4x^3+9x^2$  

•  $4x^2+9x$  

•  $4x^2+5$  

 $Find\ derivative\ of\ (𝑥+1)^2$  

•  $x+1$  

•  $2\left(x+1\right)$  

•  $2x$  

•  $2x\left(x+1\right)$  

Find derivative of $\sin(2𝑥)$  

•  $−2\sin(2𝑥)$  

•  $2\cos(2𝑥)$  

•  $2\cos𝑥\sin x$  

•  $−2\cos𝑥\sin x$  

find derivative of  $\sin^2\ x$  

•  $2\cos(2𝑥)$  

•  $2\cos𝑥\sin x$  

•  $−2\sin(2𝑥)$  

•  $−2\cos𝑥\sin x$  

Find the derivative of

 $\frac{d}{dx}\tan x$  

•  $\operatorname{cosec}x\cot x$ 

•  $\sec x\ \tan x\$  

•  $\sec2x$  

•  $-\operatorname{cosec}x\cot x\$  

Find the derivative of

 $\frac{d}{dx}\cos x$  

•  $\sin x$  

•  $-\sin x$ 

•  $-\operatorname{cosec}x\cot x$  

•  $\sec2x$ 

What is the derivative of y = 2π ?

• 0

• 2

• -2

• None of the above

In what value of x will the following function discontinuous?

• -1

• -2

• -3

• -4