Calculus 1 Exam Review Part8

In this live stream, we will review various problems likely to appear in your Final Exam.
Calculus 1 Exam Review
Continuity Problem 1: Determine if the following function is continuous at x=0. If not, determine the type of discontinuity it has:

g(x) = \left \{\begin{array}{ll} \frac{ x + 4x^2 + 3x^3 }{ x^2 } &\,\, \hbox{if} \,\, x\neq0
6x-1&\,\, \hbox{if} \,\, x = 0
\end{array} \right.


In problem 1: Find the antiderivative of the function sec^2( x ) tan(x)^(5).


Problem 2: Compute the following limit.
\lim_{x \rightarrow 2 }\frac{-2 + x}{\sqrt{14 + x}-4}= ? \no



Problem 3: Compute the following limit.
\lim_{x \rightarrow -9 }\frac{18 + 2x -18x^2 -2x^3}{81 + 18x + x^2}

Problem 3: Find derivative of f(x) = \frac{ 8x-10 }{ -5x-10 } using the definition.
Continuity Problem 1: Determine if the following function is continuous at x=5. If not, determine the type of discontinuity it has:

g(x) = \left \{\begin{array}{ll} \frac{ 5 -x }{ -10 -8x -8x^2 + 2x^3 } &\,\, \hbox{if} \,\, x\neq5
-5x+3&\,\, \hbox{if} \,\, x = 5
\end{array} \right.





Problem 5


-9y^3x^2+6y^2x+2y = \csc( y ) .


\frac{ dy }{ dx } = \,\, ?


Indeterminate Form: Compute the limit \lim_{x\to 0^+} \frac{ \tan(4x) }{ (-8)\tan(x) } .
Problem 7 \frac{d}{dx}\bigg( 9x^3+8x^2-7x+4 \bigg). Find the tangent line at x = 1.
Problem 8 Determine the derivative \frac{d}{dx}\bigg( \tan(x)^{\ln(x)} \bigg)
Continuity Problem 1: Determine if the following function is continuous at x=-6. If not, determine the type of discontinuity it has:

g(x) = \left \{\begin{array}{ll} \frac{ -6 -x }{ -18 + 2x + 4x^2 } &\,\, \hbox{if} \,\, x\neq-6
-5x-4&\,\, \hbox{if} \,\, x = -6
\end{array} \right.


In problem 9: Find the antiderivative of the function ( 1 / x )ln(x).


Problem 10: Compute the following limit.
\lim_{x \rightarrow -3 }\frac{3 + x}{\sqrt{19 + x}-4}= ? \no



Problem 11: Compute the following limit.
\lim_{x \rightarrow 4 }\frac{-12 + 3x + 4x^2 -x^3}{4 -x}

Problem 3: Find derivative of f(x) = \frac{ 3x+5 }{ 8x-10 } using the definition.
Continuity Problem 1: Determine if the following function is continuous at x=6. If not, determine the type of discontinuity it has:

g(x) = \left \{\begin{array}{ll} \frac{ -6 -5x + 13x^2 -2x^3 }{ 36 -12x + x^2 } &\,\, \hbox{if} \,\, x\neq6
4x+8&\,\, \hbox{if} \,\, x = 6
\end{array} \right.





Problem 13


-3y^3x^2+5y^2x+3y = e^{ y }.


\frac{ dy }{ dx } = \,\, ?


Indeterminate Form: Compute the limit \lim_{x\to 0^+} \frac{ \cos(5x)+(-1)e^{ -5x } }{ (-5)\sin(x) } .
Problem 15 \frac{d}{dx}\bigg( 3x^3+7x^2-8x+4 \bigg). Find the tangent line at x = 0.
Problem 16 Determine the derivative \frac{d}{dx}\bigg( \tan(x)^{\cos(x)} \bigg)
Continuity Problem 1: Determine if the following function is continuous at x=-2. If not, determine the type of discontinuity it has:

g(x) = \left \{\begin{array}{ll} \frac{ -6 -7x -4x^2 -x^3 }{ -2 -x } &\,\, \hbox{if} \,\, x\neq-2
-8x-1&\,\, \hbox{if} \,\, x = -2
\end{array} \right.


In problem 17: Find the antiderivative of the function sin(x)((-1)sin(cos(x))).


Problem 18: Compute the following limit.
\lim_{x \rightarrow 1 }\frac{-1 + x}{\sqrt{48 + x^2}-7}= ? \no



Problem 19: Compute the following limit.
\lim_{x \rightarrow 7 }\frac{7 + 6x -15x^2 + 2x^3}{7 -x}

Problem 3: Find derivative of f(x) = \frac{ 3x-5 }{ -4x-10 } using the definition.
Continuity Problem 1: Determine if the following function is continuous at x=7. If not, determine the type of discontinuity it has:

g(x) = \left \{\begin{array}{ll} \frac{ 7 -x }{ 14 -30x -10x^2 + 2x^3 } &\,\, \hbox{if} \,\, x\neq7
-7x-8&\,\, \hbox{if} \,\, x = 7
\end{array} \right.





Problem 21


6y^3x^2+5y^2x+5y = \cot(y).


\frac{ dy }{ dx } = \,\, ?


Indeterminate Form: Compute the limit \lim_{x\to 0^+} \frac{ \ln(\tan(x)+1) }{ (-4)\tan(x) } .
Problem 23 \frac{d}{dx}\bigg( -10x^2-10x+3 \bigg). Find the tangent line at x = 2.
Problem 24 Determine the derivative \frac{d}{dx}\bigg( x^2^{e^{ x \bigg)
Continuity Problem 1: Determine if the following function is continuous at x=6. If not, determine the type of discontinuity it has:

g(x) = \left \{\begin{array}{ll} \frac{ 36 -12x + x^2 }{ 12 -20x + 15x^2 -2x^3 } &\,\, \hbox{if} \,\, x\neq6
5x+7&\,\, \hbox{if} \,\, x = 6
\end{array} \right.


In problem 25: Find the antiderivative of the function csc^2( x ) ((-1)sin(cot(x))).


Problem 26: Compute the following limit.
\lim_{x \rightarrow -2 }\frac{\sqrt{66 + x}-8}{2 + x}= ? \no



Problem 27: Compute the following limit.
\lim_{x \rightarrow 8 }\frac{8 -x}{-16 -6x -23x^2 + 3x^3}

Problem 3: Find derivative of f(x) = \frac{ -3x-2 }{ 2x-1 } using the definition.
Continuity Problem 1: Determine if the following function is continuous at x=1. If not, determine the t