Precalculus Solutions | Expert Assistance for Problems & Examples

How to show $\sec^{- 1} (1 + x) = O (x^{\frac{1}{2}})$ as $x \to 0$
According to the definition, I have to find the positive constant C, i.e., I want to obtain:
$lim_{x \to 0} | \frac{\sec^{- 1} (1 + x)}{x^{\frac{1}{2}}} | = C$
Now use the L'hospital's rule:
$lim_{x \to 0} | \frac{\sec^{- 1} (1 + x)}{x^{\frac{1}{2}}} | = lim_{x \to 0} | \frac{\frac{1}{(1 + x) \sqrt{{(1 + x)}^{2} - 1}}}{\frac{1}{2} x^{- \frac{1}{2}}} | = lim_{x \to 0} | \frac{2 x^{\frac{1}{2}}}{(1 + x) \sqrt{{(1 + x)}^{2} - 1}} |$

Aldo Fernandez 2022-04-07

How to prove that $\sin^{4} (x)$ is even
Function is even when f(x)=f(-x), so my aim is to prove that $\sin^{4} (x)$ is even. So I could write it like $\sin^{4} (- x)$ which, in turn, is $(- \sin (x)) \times (- \sin (x)) \times (- \sin (x)) \times (- \sin (x))$ and equal to the one with positive x. Is that enough prove or I should expose it in some other way?

Mary Bates 2022-04-07

How to prove $\frac{1 + \tan x}{1 - \tan x} = \frac{\sec^{2} x + 2 \tan x}{2 - \sec^{2} x}$

Aileen Rogers 2022-04-07

How to proof: $\cos (10^{\circ}) \cdot \cos (30^{\circ}) \cdot \cos (50^{\circ}) \cdot \cos (70^{\circ}) = \frac{3}{16}$

Quinn Moses 2022-04-07

How to integrate this?
$\int \sec^{2} (3 x) e^{\tan (3 x)} d x$

Boston Fitzgerald 2022-04-07

What is the easiest way to solve this trigonometric equation?
$- \sin x - \sin 8 x = \sin 9 x$

daurialebraslmc 2022-04-06

Finding:
$\int_{- \infty}^{\infty} \frac{x^{2}}{x^{4} + 1}$

runddansm88e 2022-04-06

Finding the root mean square of a sum of trig functions
$v (t) = 3 - 2 \sin (t) + 8 \sin^{2} (t)$

Braden Hatfield 2022-04-06

Finding roots of the fourth degree polynomial:
$2 x^{4} + 3 x^{3} - 11 x^{2} - 9 x + 15 = 0$

George Michael 2022-04-06

Finding sum of $\sum_{{x = 1}}^{17} \frac{1}{1 + \cot^{4} (10^{\circ} x)}$

Sebastian Fox 2022-04-06

Finding $lim_{x \to π} \frac{\sin 5 x}{x - π}$ without using L'Hostpital's rule

Marshall Wolf 2022-04-06

Finding $(\frac{1}{2} + \cos \frac{π}{20}) (\frac{1}{2} + \cos \frac{3 π}{20}) (\frac{1}{2} + \cos \frac{9 π}{20}) (\frac{1}{2} + \cos \frac{27 π}{20})$

Nevaeh Glass 2022-04-06

Finding exact value of trigonometric functions
$\cos (\sin^{- 1} (\frac{12}{13}) + \sin^{- 1} (\frac{4}{5}))$

Reagan Gomez 2022-04-06

Find undetermined coefficients in polynomial quotient and remainder
$P (x) = x^{4} - 6 x^{3} + 16 x^{2} - 25 x + 10$

Nevaeh Glass 2022-04-06

Find traingle ABC satisfies
$1 + 2 \sqrt{2} \sin \frac{B}{2} \sin \frac{C}{2} = \cos B + \cos C$

Reagan Gomez 2022-04-06

Find the y-coordinate given $\cos θ + \sin^{2} θ = - \frac{5}{16}$

Dakota Livingston 2022-04-06

If
$\frac{3 - \tan^{2} \frac{π}{7}}{1 - \tan^{2} \frac{π}{7}} = α \cos \frac{π}{7}$

Alan Zavala 2022-04-06

I'm trying to integrate:
$\int \frac{8 d x}{3 \cos 2 x + 1}$

River Dudley 2022-04-06

I'm struggling to establish the identity below:
$\tan u (\csc u - \sin u) = \cos u$

Trent Fuller 2022-04-06

I'm supposed to show that:
$y = \frac{5 (x - 1) (x + 2)}{(x - 2) (x + 3)} = P + \frac{Q}{(x - 2)} + \frac{R}{(x + 3)}$

Precalculus problems and solutions are hard to find online even though this topic is quite popular among college students majoring in Engineering. Keeping this fact in mind, we decided to provide you with a list of questions and answers that will help you with various precalculus problems. Regardless if it is related to equations or any other problem, these precalculus problems and composite functions examples and solutions below will help you see the logic and compare solutions as you check your original task.

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