Calculus Bowl 1

Front

What is the derivative of the function y = 3x^2 - 4x + 2?

Back

6x - 4

Front

Evaluate the limit: \lim_{x \rightarrow \infty} \left( \frac{3x^2 + 4}{2x^2 - 7x + 4} \right)

Back

\frac{3}{2}

Front

Evaluate the limit: \lim_{x \rightarrow \infty} \left( \frac{5x^2 + 7x - 9}{-6x^2 + 2} \right)

Back

-\frac{5}{6}

Front

What is the derivative of the function f(x) = 1 - x^2?

Back

-2x

Front

Define the derivative in calculus.

Back

The derivative measures how a function changes as its input changes, representing the slope of the tangent line to the function's graph.

Front

What is the limit of a function as x approaches infinity?

Back

The limit describes the behavior of a function as the input grows without bound.

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = n*x^(n-1).

Front

What does it mean for a limit to not exist?

Back

A limit does not exist if the function approaches different values from different directions or if it grows without bound.

Front

What is the quotient rule for derivatives?

Back

If f(x) = \frac{g(x)}{h(x)}, then f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{(h(x))^2}.

Front

What is the significance of the limit in calculus?

Back

Limits are fundamental in defining derivatives and integrals, helping to understand the behavior of functions.