lim ⁡ x → 4 1 − 2 x = \lim_{x\rightarrow4}\sqrt{1-2x}= x → 4 lim 1 − 2 x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> =

− 7 \sqrt{-7} − 7 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

The function f(x) is continuous over the interval [3, 8] and f ( 3 ) = − 2 f\left(3\right)=-2 f ( 3 ) = − 2 and f ( 8 ) = 5 f\left(8\right)=5 f ( 8 ) = 5 . Check all of the following that must be true.

There is some value of x on the interval [3, 8] such that f(x) = 3

There is some value of x on the interval [3, 8] such that f(x) = 10

If "c" is on the interval [3, 8] then, − 2 ≤ f ( c ) ≤ 5 -2\le f\left(c\right)\le5 − 2 ≤ f ( c ) ≤ 5

Given this table, what limits are most accurate?

As x approaches 3 from the left, the limit is negative infinity & as x approaches 3 from the right, the limit is infinity

As x approaches 3, the limit is infinity

As x approaches 3, the limit is negative infinity

As x approaches 3 from the left, the limit is infinity and as x approaches 3 from the right, the limit is negative infinity

Given a continuous function on the interval [4,7]. Let's say that f(4) = 10 and f(7) = 20. Is there a value on the interval [4,7] where f(x) = 15?

Yes - if the function is continuous, then there must be an x value on that interval that passes through 15 on its way from 10 to 20.

No because there is no sign change on the interval [4,7].

No because that would be just too good to be true.

For a function to be continuous on an interval, which of the following must be true?

f ( a ) f\left(a\right) f ( a ) is defined

lim ⁡ x → a f ( x ) \lim_{x\rightarrow a}f\left(x\right) x → a lim f ( x ) exists

f ( a ) = lim ⁡ x → a f ( x ) f\left(a\right)=\lim_{x\rightarrow a}f\left(x\right) f ( a ) = x → a lim f ( x )

The function, f , is defined. Which of the following statements is true?

f f has a removeable discontinunity at x=2 x = 2

f f f is continuous at x = 2 x=2 x = 2

f f has a jump discontinunity at x=2 x = 2

f f has a discontinuity due to a vertical asymptote at x=2 x = 2

AP Calc AB Unit 1 Review

Authored by Caitlin Smith

Mathematics

12th Grade

CCSS covered

Used 43+ times

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27 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find f(2).

-1

DNE

Tags

CCSS.HSF.IF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the limit of the function as x approaches 2⁺.

-1

DNE

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the limit?

DNE

Infinity

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the limit?

DNE

2/3

1/4

Infinity

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the limit of f(x) as x approaches c from the right?

-4

DNE

Tags

CCSS.HSA.REI.D.10

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\lim_{x\rightarrow4}\sqrt{1-2x}=$

DNE

$\sqrt{-7}$

$\infty$

$-\infty$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\lim_{x\rightarrow\pm\infty}\ \frac{2x^2+3}{5x^2+7}$

$\pm\propto$

$\frac{2}{5}$

$\frac{3}{7}$

$\frac{\infty}{\infty}$

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AP Calc AB Unit 1 Review

Find f(2).

Find the limit of the function as x approaches 2⁺.

What is the limit?

What is the limit?

What is the limit of f(x) as x approaches c from the right?

$\lim_{x\rightarrow4}\sqrt{1-2x}=$

$\lim_{x\rightarrow\pm\infty}\ \frac{2x^2+3}{5x^2+7}$

Find the limit as x approaches 1⁺

Select all statements that are TRUE.

Determine whether the graph of the function has a vertical asymptote or a removeable discontinuity at x = -1.

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

AP Calc AB Unit 1 Review

Find f(2).

Find the limit of the function as x approaches 2+.

What is the limit?

What is the limit?

What is the limit of f(x) as x approaches c from the right?

lim⁡x→41−2x=\lim_{x\rightarrow4}\sqrt{1-2x}=x→4lim​1−2x​=

lim⁡x→±∞ 2x2+35x2+7\lim_{x\rightarrow\pm\infty}\ \frac{2x^2+3}{5x^2+7}x→±∞lim​ 5x2+72x2+3​

Find the limit as x approaches 1+

Select all statements that are TRUE.

Determine whether the graph of the function has a vertical asymptote or a removeable discontinuity at x = -1.

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Find the limit of the function as x approaches 2⁺.

$\lim_{x\rightarrow4}\sqrt{1-2x}=$

$\lim_{x\rightarrow\pm\infty}\ \frac{2x^2+3}{5x^2+7}$

Find the limit as x approaches 1⁺