By the end of Calculus II, students should have significant **fundamental knowledge and skills** so they can apply calculus to future STEM academic training and professional practice.

**Fundamental calculus knowledge and skills** will be learned and evaluated based on specific objectives related to:

- Apply L'Hospital's Rule to calculate limits of various indeterminate forms.
- Calculate derivatives of:
- inverse trigonometric functions,
- hyperbolic trigonometric functions,
- exponential and logarithmic functions.
- Recognize when to apply logarithmic differentiation.
- Calculate slope of tangent lines for curves given parametrically or in polar coordinates.

- Calculate volumes of solids of revolution.
- Apply integration to force functions to calculate work.
- Apply exponentials to solve real world problems such as: population growth, decay of radioactive elements, and Newton's Law of Cooling.
- Solve initial value problems for separable differential equations.
- Recognize when to apply integration techniques such as:
- integration by parts,
- trigonometric substitution,
- partial fractions.

- Compute arc length of a function given:
- in Cartesian coordinates,
- in polar coordinates,
- parametrically.

- Solve for the area between polar curves.

- Determine the limit of a sequence by applying previous calculus knowledge.
- Calculate the limit of a geometric series.
- Apply tests to determine convergence/divergence of series including:
- n-th term test,
- p-series test,
- alternating series test,
- ratio test,
- integral test,
- comparison tests.

- Apply the ratio test to determine the interval of convergence for a power series.
- Memorize common power series representations of functions.
- Determine power series representations of more complicated functions by manipulating known power series representations.
- Apply the Taylor series formula to calculate even more power series representations of various functions.

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