Calculus Problems

Calculus is a branch of mathematics that deals with rates of change and accumulation. Here are some common problems you might encounter in calculus:

Differentiation

1. Find the derivative of ( f(x) = x^2 ).

   • Solution: ( f'(x) = 2x )

2. Differentiate ( g(x) = \sin(x) ).

   • Solution: ( g'(x) = \cos(x) )

Integration

1. Integrate ( \int x^3 dx ).

   • Solution: ( \frac{x^4}{4} + C )

2. Find ( \int \cos(x) dx ).

   • Solution: ( \sin(x) + C )

Limits

1. Evaluate ( \lim_{x \to 0} \frac{\sin(x)}{x} ).

   • Solution: 1

2. Find ( \lim_{x \to \infty} (2x + 3) ).

   • Solution: ( \infty )

For more in-depth understanding and practice, check out our Calculus Study Guide.

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