Calculus 1 Exam Review Part7

In this live stream, we will review various problems likely to appear in your Final Exam.
Calculus 1 Exam Review
In problem 1: Find the antiderivative of the function sec^2( x ) cos(tan(x)).


Problem 2: Compute the following limit.
\lim_{x \rightarrow -1 }\frac{1 + x}{\sqrt{15 + x^2}-4}= ?



Problem 3: Compute the following limit.
\lim_{x \rightarrow -5 }\frac{20 + 14x + 17x^2 + 3x^3}{-5 -x}

Problem 3: Find derivative of f(x) = \frac{ 2x-9 }{ 3x+6 } using the definition.
Problem 5: Find the derivative of f(x) = \tan(x)\ln(x) , using derivative rules.
Problem sec(x): Find the derivative of the function f of x equal to the quotient of sec(x)/exp(x).



Problem 7


-2y^3x^2+2y^2x = \ln(y).


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


Indeterminate Form: Compute the limit \lim_{x\to 0^+} \frac{ \ln(\tan(4x)+1) }{ (-7)\tan(x) } .
Problem 9 \[ \frac{d}{dx}\bigg( -3x^2-2x+1 \bigg). \] Find the tangent line at x = 0.
Problem 10 Determine the derivative \frac{d}{dx}\bigg( \tan(x)^{ \sec( x ) } \bigg)
In problem 11: Find the antiderivative of the function sin(x)((-1)sin(cos(x))).


Problem 12: Compute the following limit.
\lim_{x \rightarrow -4 }\frac{\sqrt{53 + x}-7}{4 + x}= ?



Problem 13: Compute the following limit.
\lim_{x \rightarrow -7 }\frac{49 + 14x + x^2}{28 + 18x + 9x^2 + x^3}

Problem 3: Find derivative of f(x) = \frac{ 7x+1 }{ -4x-6 } using the definition.
Problem 15: Find the derivative of f(x) = \sec( x ) e^{ x } , using derivative rules.
Problem exp(x): Find the derivative of the function f of x equal to the quotient of exp(x)/tan(x).



Problem 17


-4y^3x^2+5y^2x+8y = \csc( y ) .


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


Indeterminate Form: Compute the limit \lim_{x\to 0^+} \frac{ \ln(\sin(4x)+1) }{ (-3)\sin(x) } .
Problem 19 \[ \frac{d}{dx}\bigg( 6x^2+4x-4 \bigg). \] Find the tangent line at x = 1.
Problem 20 Determine the derivative \frac{d}{dx}\bigg( \sin(x)^{\ln(x)} \bigg)
In problem 21: Find the antiderivative of the function csc^2( x ) ((-1)cos(cot(x))).


Problem 22: Compute the following limit.
\lim_{x \rightarrow 3 }\frac{-3 + x}{\sqrt{x^2}-3}= ?



Problem 23: Compute the following limit.
\lim_{x \rightarrow 3 }\frac{9 + 6x -9x^2 + 2x^3}{3 -x}

Problem 3: Find derivative of f(x) = \frac{ 2x-1 }{ -9x-6 } using the definition.
Problem 25: Find the derivative of f(x) = \tan(x)\ln(x) , using derivative rules.
Problem ln(x): Find the derivative of the function f of x equal to the quotient of ln(x)/cos(x).



Problem 27


-3y^3x^2-5y^2x-5y = \csc( y ) .


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


Indeterminate Form: Compute the limit \lim_{x\to 0^+} \frac{ \tan(2x) }{ (-8)\tan(x) } .
Problem 29 \[ \frac{d}{dx}\bigg( -7x^3-6x^2+8x-8 \bigg). \] Find the tangent line at x = 0.
Problem 30 Determine the derivative \frac{d}{dx}\bigg( x^2^{\cot(x)} \bigg)
In problem 31: Find the antiderivative of the function sec( x ) tan( x ) sec( x ) ^(3).


Problem 32: Compute the following limit.
\lim_{x \rightarrow 0 }\frac{\sqrt{x{x}= ?



Problem 33: Compute the following limit.
\lim_{x \rightarrow 0 }\frac{-x}{-x^2 + x^3}

Problem 3: Find derivative of f(x) = \frac{ 7x+3 }{ -5x+5 } using the definition.
Problem 35: Find the derivative of f(x) = \ln(x)\sin(x) , using derivative rules.
Problem sec(x): Find the derivative of the function f of x equal to the quotient of sec(x)/exp(x).



Problem 37


6y^3x^2-1y^2x+4y = \ln(y).


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


Indeterminate Form: Compute the limit \lim_{x\to 0^+} \frac{ \tan(2x) }{ (-3)\tan(x) } .
Problem 39 \[ \frac{d}{dx}\bigg( -6x^3+6x^2+6x+8 \bigg). \] Find the tangent line at x = 0.
Problem 40 Determine the derivative \frac{d}{dx}\bigg( x^2^{\cot(x)} \bigg)