Given the function $f\left(x\right)=x^2+3x$, what is the slope of the line tangent to the curve at the point $x=2$?

In Exercises 83–88, find equations for the lines that are tangent, and the lines that are normal, to the curve at the given point.

(y - x)² = 2x + 4, (6, 2)

In Exercises 83–88, find equations for the lines that are tangent, and the lines that are normal, to the curve at the given point.

x³/² + 2y³/² = 17, (1, 4)

For Exercises 55 and 56, evaluate each limit by first converting each to a derivative at a particular x-value.

lim (x → 1) (x⁵⁰ − 1) / (x − 1)

For Exercises 55 and 56, evaluate each limit by first converting each to a derivative at a particular x-value.

lim (x → −1) (x²/⁹ − 1) / (x + 1)

For what value of $x$ is the tangent line to the function $f\left(x\right)=x^3-3x^2+2$ horizontal?

Which of the following is an equation of the line tangent to the graph of $y=\cos x$ at $x=\frac{\pi }{2}$?

What is the slope of the tangent line to the curve $y^3-x{y}^2+x^3=5$ at the point $(1,2)$?

What is the slope of the tangent line to the curve $x^2+y^2=2$ at the point $(1,1)$?