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$\int e^{x} [\frac{(\sin^{- 1} x) \sqrt{1 - x^{2}} + 1}{\sqrt{1 - x^{2}}}] d x$ ?

Dexter Odom 2022-03-28

Differentiate f(x)=2x-3 using first principal?

abitinomaq1 2022-03-28

Determine whether the function $f (x) = \frac{x - 1}{x + 52}$ is concave up or concave down and its intervals?

Dexter Odom 2022-03-28

Derivation of the tangent half angle identity
I'm having trouble proceeding from
$\frac{\sin (θ)}{1 + \cos (θ)}$
to
$\tan (\frac{θ}{2})$
Context:
Consider the function f defined for all (x,y) such that $y \neq 0$ with the rule
$f (x, y) = \frac{y}{\sqrt{x^{2} + y^{2}} + x}$
Show that
$f (r \cos (θ), r \sin (θ)) = \tan (\frac{θ}{2})$
So far I've done:
$f (r \cos (θ), r \sin (θ)) = \frac{r \sin (θ)}{\sqrt{r^{2} \cos^{2} (θ) + r^{2} \sin^{2} (θ)} + r \cos (θ)} = \frac{r \sin (θ)}{\sqrt{r^{2}} + r \cos (θ)}$
$= \frac{\sin (θ)}{1 + \cos (θ)}$
Using
$\cos (θ) = 2 \cos^{2} (\frac{θ}{2}) - 1 \Rightarrow 2 \cos^{2} (\frac{θ}{2}) = \cos (θ) + 1$
We get
$f (r \cos (θ), r \sin (θ)) = \frac{\sin (θ)}{2 \cos^{2} (\frac{θ}{2})}$

Rex Maxwell 2022-03-28

Use L'Hospital Rule to find the limits
$lim_{x \to 0} \frac{\sin m x}{\sin n x}$

Marzadri9lyy 2022-03-28

Evaluate the following limits.
$lim_{θ \to 0} \frac{\sec θ - 1}{θ}$

calcolare45pj 2022-03-28

Find the limits:
$lim_{x \to 2} \frac{\sqrt{x^{2} + 12} - 4}{x - 2}$

tambustqaze 2022-03-27

Consider the function $f (x) = - 3 x^{3} - 4 x^{2} - 3 x + 3$ on the interval [2,4], how do you find the average or mean slope of the function on this interval?

Coradossi7xod 2022-03-27

compute the limit of
$lim_{x \to \frac{π}{3}} \frac{1 - 2 \cos (x)}{\sin (3 x)}$
I would like to not do a translation with the change of variable $t = x - \frac{π}{3}$

alparcero97oy 2022-03-27

How do I find concave up and concave down from $f (x) = x^{3} + 3 x^{2} + 5 x + 7$ ?

Lesnaoq73 2022-03-27

How can I prove that
$lim_{(x, y) \to (0, 0)} \frac{{| x |}^{\frac{3}{2}} y^{2}}{x^{4} + y^{2}} \to 0$

Erik Cantu 2022-03-27

How can I calculate the following difficult limit: $lim_{x \to \infty} (x + \sin x) \sin \frac{1}{x}$ ?

zatajuxoqj 2022-03-27

Help showing $\int_{0}^{1} \frac{d x}{x \log \frac{1}{x}}$ is unbounded

kembdumatxf 2022-03-27

For what values of x is $f (x) = 3 x^{3} - 7 x^{2} - 5 x + 9$ concave or convex?

talpajocotefnf3 2022-03-27

For what values of x is $f (x) = 2 x^{4} + 4 x^{3} + 2 x^{2} - 2$ concave or convex?

Polchinio3es 2022-03-27

For what values of x is $f (x) = \frac{4}{x^{2}} + 1$ concave or convex?

Reuben Brennan 2022-03-26

Determine whether the function $f (x) = \frac{x}{x^{2} + 2}$ is concave up or concave down and its intervals?

Marzadri9lyy 2022-03-26

Help solving another integral
$\int {(2 x^{2} + 4 x - 2)}^{- \frac{3}{2}} d x$

Kiara Haas 2022-03-26

For what values of x is $f (x) = \frac{4}{x^{2} - 1}$ concave or convex?

ICESSRAIPCELOtblt 2022-03-26

For what values of x is $f (x) = x^{4} - x^{3} + 7 x^{2} - 2$ concave or convex?

The majority of Calculus 1 questions and answers that you will find below should be sufficient for understanding the basic rules that are necessary for problem-solving purposes. Take a look at the original answers, seek math assignment help, and compare them to what you have for your assignment.

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