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Calculus with Applications

Evaluate each integral.
$$\int_{2}^{7} \frac{3+5 y}{\sqrt{x}} d y$$

Multivariable Calculus
Double Integrals
Matt J.
Calculus with Applications

Evaluate each integral.
$$\int_{-1}^{1} e^{2 x+3 y} d y$$

Multivariable Calculus
Double Integrals
Matt J.
Thomas Calculus

Determine the values of constants $a, b, c,$ and $d$ so that
$f(x)=a x^{3}+b x^{2}+c x+d$ has a local maximum at the point
$(0,0)$ and a local minimum at the point $(1,-1)$ .

Applications of Derivatives
Monotonic Functions and the First Derivative Test
Matt J.
Calculus of a Single Variable

In Exercises 21-28, use the graph to find the limit (if it exists). If the limit does not exist, explain why.$$\lim _{x \rightarrow 5} \frac{2}{x-5}$$

Limits and Their Properties
Finding Limits Graphically and Numerically
Calculus of a Single Variable

Acceleration Assume that a fully loaded plane starting from rest has a constant acceleration while moving down a runway. The plane requires 0.7 mile of runway and a speed of 160 miles per hour in order to lift off. What is the plane's acceleration?

Antiderivatives and Indefinite Integration
Allan H.
Calculus of a Single Variable

Sketching the Graph of a Trigonometric Function In Exercises $55-66,$ sketch the graph of the function.
$$y=2 \cos 2 x$$

Preparation for Calculus
Review of Trigonometric Functions
Noah C.
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