Calculus Practice Questions

Find the derivative of ( f(x) = ln(x) ).

What is the integral of the constant function ( f(x) = 5 )?

Evaluate the limit ( lim_ (2x^2 + 3x + 1(x^2 + 1) ).

How do you find the critical points of ( f(x) = x^2 - 4x + 4 )?

What is the derivative of ( f(x) = cos(x) )?

Find the antiderivative of ( f(x) = x^3 ).

Evaluate the definite integral ( int_1^3 x , dx ).

What is the limit of ( tan(x) ) as ( x ) approaches ( frac ) from the left?

How do you find the inflection points of ( f(x) = x^3 - 6x^2 + 9x )?

What is the derivative of ( f(x) = sin^(x) )?

Find the integral of ( f(x) = frac ).

Evaluate the limit ( lim_ frac ).

How do you determine if ( f(x) = x^4 - 4x^2 ) has a local maximum or minimum at ( x = 0 )?

What is the derivative of ( f(x) = ln|x| )?

Find the derivative of ( f(x) = tan(x) ).

What is the integral of ( f(x) = x^n ) where ( n eq -1 )?

Evaluate the definite integral ( int_0^1 (2x^3 - x) , dx ).

What is the limit of ( frac ) as ( x ) approaches 1?

How do you find the slope of the tangent line to ( f(x) = x^2 + 2x ) at ( x = 3 )?

What is the derivative of ( f(x) = sec(x) )?

Find the antiderivative of ( f(x) = cos(x) ).

Evaluate the limit ( lim_ frac ).

How do you find the local extrema of ( f(x) = x^3 - 3x^2 + 4 )?

What is the derivative of ( f(x) = csc(x) )?

Find the integral of ( f(x) = sin(x) ).

What is the limit of ( frac ) as ( x ) approaches infinity?

How do you find the points of inflection for ( f(x) = x^4 - 4x^3 + 6x^2 )?

What is the derivative of ( f(x) = tan^(x) )?

Find the antiderivative of ( f(x) = e^x ).

Evaluate the definite integral ( int_0^pi sin(x) , dx ).

What is the limit of ( frac ) as ( x ) approaches infinity?

How do you determine concavity for ( f(x) = x^3 - 3x )?

What is the derivative of ( f(x) = sinh(x) )?

Find the integral of ( f(x) = cosh(x) ).

Evaluate the limit ( lim_ frac ).

How do you find the asymptotes of ( f(x) = frac )?

What is the derivative of ( f(x) = cosh^(x) )?

Find the antiderivative of ( f(x) = frac ).

What is the limit of ( frac ) as ( x ) approaches 0?

How do you find the derivative of ( f(x) = x^x )?

What is the derivative of ( f(x) = ln(x^2 + 1) )?

Find the integral of ( f(x) = frac ).

Evaluate the definite integral ( int_0^1 sqrt , dx ).

What is the limit of ( frac ) as ( x ) approaches infinity?

How do you find the local extrema of ( f(x) = x^4 - 8x^2 + 16 )?

What is the derivative of ( f(x) = cos^(x) )?

Find the antiderivative of ( f(x) = tan(x) ).

Evaluate the limit ( lim_ frac ).

How do you find the vertical asymptotes of ( f(x) = frac )?

What is the derivative of ( f(x) = sinh^(x) )?

Find the integral of ( f(x) = sec^2(x) ).

What is the limit of ( frac ) as ( x ) approaches 2?

How do you find the derivative of ( f(x) = sqrt )?

What is the derivative of ( f(x) = cot(x) )?

Find the antiderivative of ( f(x) = frac} ).

Evaluate the definite integral ( int_0^1 (x^2 + 2x + 1) , dx ).