Evaluate lim ⁡ θ → π 6 cos ⁡ 2 θ sin ⁡ θ tan ⁡ θ \lim_{\theta\rightarrow\ \frac{\pi}{6}}\ \frac{\cos\ 2\theta}{\sin\ \theta\ \tan\ \theta} θ → 6 π lim sin θ tan θ cos 2 θ . (set your calculator in radian mode)

3 \sqrt{3} 3 <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">

Which of the given conditions does NOT satisfy the continuity of the given function?

lim ⁡ x → 2 − h ( x ) = 4 \lim_{x\rightarrow2^-}h\left(x\right)=4 x → 2 − lim h ( x ) = 4

h ( 2 ) = 5 h\left(2\right)=5 h ( 2 ) = 5

lim ⁡ x → 2 + h ( x ) = 5 \lim_{x\rightarrow2^+}h\left(x\right)=\ 5 x → 2 + lim h ( x ) = 5

h ( 2 ) = lim ⁡ x → 2 h ( x ) h\left(2\right)=\lim_{x\rightarrow2}\ h\left(x\right) h ( 2 ) = x → 2 lim h ( x )

Which of the following intervals does NOT belong to the group?

( 0 , 3 ) \left(0,3\right) ( 0 , 3 )

( − ∞ − 3 ) \left(-\infty-3\right) ( − ∞ − 3 )

( − 3 , 0 ) \left(-3,0\right) ( − 3 , 0 )

[ 0.3 ) \left[0.3\right) [ 0 . 3 )

Which of the following intervals does NOT belong to the group?

( 0 , 0 ) \left(0,0\right) ( 0 , 0 )

[ 0 , 3 ) \left[0,3\right) [ 0 , 3 )

( 3 , 6 ] \left(3,6\right] ( 3 , 6 ]

( 6 , + ∞ ) \left(6,+\infty\right) ( 6 , + ∞ )

Consider the given graph. What type of discontinuity is x = 0 in the given function f?

infinite/essential discontinuity

Prove that the given number of the function is discontinuous . Which of the conditions is FALSE?

lim ⁡ x → − 6 3 x + 6 E X I S T S \lim_{x\rightarrow-6}\ \frac{3}{x+6}EXISTS x → − 6 lim x + 6 3 E X I S T S

f ( − 6 ) = 1 f\left(-6\right)=1 f ( − 6 ) = 1

lim ⁡ x → − 6 − 3 x + 6 = − ∞ \lim_{x\rightarrow-6^-}\ \frac{3}{x+6}=-\infty x → − 6 − lim x + 6 3 = − ∞

lim ⁡ x → − 6 + 3 x + 6 = + ∞ \lim_{x\rightarrow-6^+}\ \frac{3}{x+6}=+\infty x → − 6 + lim x + 6 3 = + ∞

Which of the given solutions is NOT valid given the limits, lim ⁡ x → 0 1 − cos ⁡ x sin ⁡ x \lim_{x\rightarrow0}\ \frac{1\ -\ \cos\ x\ }{\sin\ x} x → 0 lim sin x 1 − cos x

= lim ⁡ x → 0 1 − cos ⁡ x x lim ⁡ x → 0 sin ⁡ x x =\frac{\lim_{x\rightarrow0}\ \frac{1-\cos x}{x}}{\lim_{x\rightarrow0}\ \frac{\sin\ x}{x}} = lim x → 0 x sin x lim x → 0 x 1 − cos x

= = lim ⁡ x → 0 ( 1 − cos ⁡ x x sin ⁡ x x ) =\lim_{x\rightarrow0}\ \left(\frac{\frac{1-\cos x}{x}}{\frac{\sin\ x}{x}}\right) = x → 0 lim ( x sin x x 1 − cos x )

LWW2: Limits of Transcendental Functions & Continuity

Authored by Peter Didulo

Mathematics

11th Grade

Used 47+ times

LWW2: Limits of Transcendental Functions & Continuity

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30 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

$\left(0,\infty\right)$

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

$\left(0,2\right)$

$\left(1,2\right)$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

$f\left(x\right)=\ x^3\left(2x^2-4x+7\right)$

$g\left(x\right)=\frac{x^2+1}{x^2-9}$

$g\left(x\right)=\frac{x-1}{x^2-5x+6}$

$h\left(x\right)=\left\{\left(x+1\right)\ if\ x<0,\ \left(x^2+1\ \right),\ if\ x\ge0\right\}$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The function f has a jump discontinuity at ________.

x = - 1

x = 0

x = 1

x = 2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The function f has a removable discontinuity at ______.

x = - 1

x = 0

x = 1

x = 2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

$-\infty$

$+\infty$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

$\infty$

$\frac{4}{25}$

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

$-\infty$

$\infty$

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LWW2: Limits of Transcendental Functions & Continuity

Which of the intervals is NOT continuous given the function f(x)=x2+x−20x−4f\left(x\right)=\frac{x^2+x-20}{x-4}f(x)=x−4x2+x−20​ ?

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

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

What is the type of discontinuity given the function f(x) = x2+x−20x−4f\left(x\right)\ =\ \frac{x^2+x-20}{x-4}f(x) = x−4x2+x−20​ ?

The function f has a jump discontinuity at ________.

The function f has a removable discontinuity at ______.

What is the point of discontinuity of the function f(x) = 1(x+2)2f\left(x\right)\ =\ \frac{1}{\left(x+2\right)^2}f(x) = (x+2)21​ ?

Evaluate lim⁡x→0 sin⁡ 5x5x\lim_{x\rightarrow0}\ \frac{\sin\ 5x}{5x}x→0lim​ 5xsin 5x​

Evaluate lim⁡x→−2 [(4)(5x)]\lim_{x\rightarrow-2}\ \ \left[\left(4\right)\left(5^x\right)\right]x→−2lim​ [(4)(5x)]

Evaluate lim⁡x→∞ e−x\lim_{x\rightarrow\infty}\ e^{-x}x→∞lim​ e−x

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Discover more resources for Mathematics

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

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

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

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

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

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

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