Horizontal Tangent Line Determine the point(s) at which the graph of $f(x)=\dfrac{x}{\sqrt{2 x-1}}$ has a horizontal tangent line.

A solution is prepared by dissolving $22.0$ g of $NaOH$ in $l18.0$ g of water. The $NaOH$ solution has a density of $1.15$ $g/mL$ What is the molarity ($M$) of the solution?

Horizontal Tangent Line Determine the point(s) in the interval $(0,2 \pi)$ at which the graph of $f(x)=2 \cos x+\sin 2 x$ has a horizontal tangent line.

Explain why the equation log (-x) = -4 does have a solution, and find that solution.

To construct chart notes, replace the italicized terms in each of the two scenarios with one of the medical terms listed below.

$$\begin{array}{lll}\text { anorexia } & \text { gastric reflux } & \text { jaundice } \\ \text { antacids } & \text { hepatomegaly } & \text { nausea } \\ \text { dyspepsia } & \text { hiatal hernia } & \text { sclerae } \\ \text { dysphagia}\end{array}$$

During her annual check-up, Mrs. L. complains that she has $(1)$ difficulty swallowing. Also, she is awakened at night with a feeling of $(2)$ difficult or painful digestion. She further complains of $(3)$ regurgitation of stomach acids and has been taking Tums and Rolaids. She feels that the $(4)$ medications to neutralize the backflow of acid from her stomach have not been effective. After a thorough examination along with some radiographic procedures, the doctor suspects her symptoms are due to a $(5)$ part of her stomach herniating up through the opening of the diaphragm.

$5$. _______.

Find all values of x (if any) where the tangent line to the graph of the given equation is horizontal. HINT [The tangent line is horizontal when its slope is zero.]

Verify the solution of the differential equation.Solution: y = 2/5(e^(-4x) + e^x) Differential Equation: y” + 4y’ = 2e^x

What is a horizontal asymptote?

Decide for what values of the constant $A$ the equation has

(a) The solution $t=0$

(b) A positive solution

(c) A negative solution

$$A^2 t^2+1=0$$

Given that $y=x$ is a solution of $x^2y''-4xy'+4y=0$, find a linearly independent solution by reducing the order. Write the general solution.

Calculate the volume in milliliters of a $1.420 \mathrm{M ~NaOH}$ solution required to titrate the following solutions:

(a) 25.00 mL of a $\mathrm{2.430 ~M~ HCl}$ solution

(b) 25.00 mL of a $4.500~ \mathrm{M ~H_2SO_4}$ solution

(c) 25.00 mL of a $1.500 ~\mathrm{M} ~\mathrm{H_3PO_4}$ solution

The graph of $y=\frac{1}{3} f(x)$ is the graph of y=f(x) with a (choose one: vertical stretch, vertical shrink, horizontal stretch, horizontal shrink).

determine the general solution of the given differential equation. y(4) − 4y” = t2 + et

One solution is $50 \%$ glycol, and another is $30 \%$ glycol. How much of each solution should be mixed to make a $100$ gallon solution that is $45 \%$ glycol?