LWW2: Limits of Transcendental Functions & Continuity

Which of the intervals is NOT continuous given the function  $f\left(x\right)=\frac{x^2+x-20}{x-4}$  ?

•  $\left(0,\infty\right)$  

•  $\left[\left(0,\infty\right)\right]$  

•  $\left(0,2\right)$  

•  $\left(1,2\right)$  

Which of the following points is NOT a point of discontinuity of   $f\left(x\right)=\sqrt{x-1}$  ?

• x = - 1

• x = -1/2

• x = 1/2

• x = 1

Which of the following functions is continuous for all real number x?

What is the type of discontinuity given the function $f\left(x\right)\ =\ \frac{x^2+x-20}{x-4}$  ?

• Jump discontinuity

• infinite discontinuity

• removable discontinuity

The function f has a jump discontinuity at ________.

• x = - 1

• x = 0

• x = 1

• x = 2

The function f has a removable discontinuity at ______.

• x = - 1

• x = 0

• x = 1

• x = 2

What is the point of discontinuity of the function $f\left(x\right)\ =\ \frac{1}{\left(x+2\right)^2}$  ?

• x = - 2

• x = 0

• x = 2

• x = 4

Evaluate  $\lim_{x\rightarrow0}\ \frac{\sin\ 5x}{5x}$  

•  $-\infty$  

• 0

• 1

•  $+\infty$  

Evaluate  $\lim_{x\rightarrow-2}\ \ \left[\left(4\right)\left(5^x\right)\right]$  

•  $\infty$  

• 0

•  $\frac{4}{25}$  

• 1

Evaluate  $\lim_{x\rightarrow\infty}\ e^{-x}$  

•  $-\infty$  

• 0

• 1

•  $\infty$