CONTINUITY AND DIFFERENTIABILITY (GAISSS)

The function f (x) = |x| + |x – 1| is

• continuous at x = 0 as well as at x = 1.

• continuous at x = 1 but not at x = 0.

• discontinuous at x = 0 as well as at x = 1.

• continuous at x = 0 but not at x = 1.

 $Iff(x)=2x\ and\ g(x)=\frac{x^2}{2}+1,\ then\ which\ of\ the\ following\ can\ be\ a\ discontinuous\ function$  

•  $f(x)+g(x)$  

•  $f(x)-g(x)$  

•  $f(x).g(x)$  

•  $\frac{f(x)}{g(x)}$  

Tags

CCSS.HSF-BF.A.1B

 $The\ function\ f(x)=\frac{4-x^2}{4x-x^3}\ is$  

•  $discontinuous\ at\ only\ one\ point\ at\ x=0$  

•  $discontinuous\ at\ exactly\ two\ points$  

•  $discontinuous\ at\ exactly\ three\ points$  

•  $continuous\ everywhere$  

Tags

CCSS.HSF-IF.C.7D

 $Find\ the\ derivative\ of\cot^2x^3$  

•  $2\cot x^3$  

•  $-2\cot x^3\operatorname{cosec}^2x^3$  

•  $-6x^2\operatorname{cosec}^2x^3.\cot x^3$  

•  $-6x^2\operatorname{cosec}^2x^3.$  

 $Is\ the\ function\ defined\ by\ f(x)=x^2–\sin x+5\ continuous\ at\ x=\pi?$  

• yes

• no

• a = 2, b = 1

• a = 1, b = 2

• a = 1, b = 3

• a = 3, b = 1

Find the derivative of

• $\frac{1}{1+x^2}$

• $\frac{2}{1+x^2}$

• $\frac{3}{1+x^2}$

• $\frac{4}{1+x^2}$

 $Find\ \ \frac{dy}{dx}\ of\ x=a\ (\cos\theta+\theta\sin\theta),y=a(\sin\theta\ –\ \theta\cos\theta)$  

•  $\sin\theta$  

•  $\cos\theta$  

•  $\tan\theta$  

•  $\cot\theta$  

 $Find\ the\ \sec ond\ order\ derivative\ of\ x^{20}$  

•  $120x^{19}$  

•  $120x^{18}$  

•  $380\ x^{18}$  

•  $380\ x^{19}$  

 $Differentiate\ \sin^2x\ w.r.t\ e^{\cos\ x}$  

•  $\frac{\cos x}{e^{\cos\ x}}$  

•  $-\frac{2\cos x}{e^{\cos x}}$  

•  $\frac{2\cos2x}{e^{\cos x}}$  

•  $-\frac{2\cos2x}{e^{\cos x}}$