Limits and Continuity — Quiz

Question 1

For which function and interval can the extreme value theorem be applied?

Revolt · Accepted Answer

f of x is equal to the fraction with numerator x and denominator open paren x minus 6 close paren squared over the interval left bracket 3 comma 5 right bracket

Question 2

Which statement describes whether the extreme value theorem applies?

Revolt · Accepted Answer

The extreme value theorem does not apply, and f of x has a maximum but not a minimum.

Question 3

Which function has a removable discontinuity at x is equal to 7 ?

Revolt · Accepted Answer

f of x is equal to the fraction with numerator x squared minus 10 x plus 21 and denominator x minus 7

Question 4

Consider the function f of x equals inequality negative the fraction with numerator 4 x and denominator x minus 3 comma x is less than 5 inequality negative 7 x plus 25 comma x is greater than 5 Which type of discontinuity occurs at x is equal to 5 ?

Revolt · Accepted Answer

endpoint

Question 5

Based on the extreme value theorem, what is the maximum value of f of x is equal to negative x squared plus 6 x over the interval left bracket 1 comma 4 right bracket ?

Revolt · Accepted Answer

9

Question 6

Function f of x is equal to the fraction with numerator 25 x and denominator x plus 3 has a discontinuity at x is equal to negative 3 What are the limits? limit x to negative 3 raised to the negative power of f times x and limit x to negative 3 raised to the plus power of f times x

Revolt · Accepted Answer

limit x to negative 3 raised to the negative power of f times x is equal to infinity limit x to negative 3 raised to the plus power of f times x is equal to negative infinity; limit x to negative 3 raised to the negative power of f times x is equal to infinity limit x to negative 3 raised to the plus power of f times x is equal to infinity

Question 7

Function f of x has a jump discontinuity at x is equal to 8 Which statement identifies possible one-sided limits at x is equal to 8 ?

Revolt · Accepted Answer

limit x to 8 raised to the negative power of f times x is equal to 85 and limit x to 8 raised to the plus power of f times x is equal to 120

Question 8

Which function is continuous at x is equal to negative 4 ?

Revolt · Accepted Answer

g of x equals inequality x squared comma x is less than negative 4 inequality negative 4 x comma x is greater than or equal to negative 4

Question 9

At which value of x does the function have a jump discontinuity?

Revolt · Accepted Answer

negative 2; 0

Question 10

Using the extreme value theorem, which graph has a maximum of 5 and minimum of negative 3 ?

Revolt · Accepted Answer

Image with description On a coordinate plane, a curve starts at closed circle (negative 2, negative 3), curves up to (1, 0.5), curves down through (0, negative 1) to (0.5, negative 1.75), and curves up to closed circle (2, 5).

Limits and Continuity — Quiz Answers

More from this Course

TRY EDGENUITY HACKS