Use numerical evidence to conjecture the value of the limit if it exists. Check your answer with your Computer Algebra System (CAS). If you disagree, which one of you is correct? $\lim _{x \rightarrow 0^{+}} x^{\ln x}$

Find the solution for the equation. $\frac { 1 } { 5 } c = 7$

Write the meaning of each italicized word in the sentences below. If necessary, consult a dictionary. (a) The hikers were able to find a pass through the mountain. (b) Were you able to pass the entrance exam for the university?

You and three friends go to a restaurant for dinner. You share three appetisers that cost $\$6$ each. You also share two desserts that cost $\$3$ each. You split the total bill evenly. How much does each person pay?

Solve these equations using any method. Check each result. a. $x^2 + 14x + 40 = 0$ b. $x^2 - 5x = 24$ c. $9x^2 = 49$ d. $x^3 - 4x = 0$

Paula is a 38-year-old administrative assistant. She visits the medical assistant at ABC Company's health office. During the interview, Paula explains she has been waking up at night with pain in both wrists. Paula also states the wrist pain becomes worse after she has been working on the computer. Paula says she has been using wrist supports but they do not seem to help. The medical assistant refers Paula to the physician. Describe the symptoms that occur in carpal tunnel syndrome.

Determine whether the statements that follow are true or false, and justify your answer: If $T$ is any linear transformation from $\mathbb{R^3}$ to $\mathbb{R^3}$, then $T (\vec{v} \times \vec{w}) = T (\vec{v}) \times T ( \vec{w})$ for all vectors $\vec{v}$ and $\vec{w}$ in $\mathbb{R^3}$.

What are the Recommended Dietary Allowances (RDAs)?

find the dervative of 3x^3

At the indicated point, compute the velocity vector, the acceleration vector, the speed, and the equation of the tangent line.
$\mathbf{c}(t) = (t^2 − 1, \cos (t^2), t^4)$, at $t =\sqrt{\pi}$

Write the first six terms of the geometric sequence with the first term, $a_{1}$, and common ratio, r. $a_{1}=2, r=3$

The family of straight lines y = ax + b (a, b arbitrary constants) can be characterized by the relation y'' = 0. Find a similar relation satisfied by the family of all circles (x - h)^2 + (y - h)^2 = r^2, where h and r are arbitrary constants. (Hint: Eliminate h and r from the set of three equations including the given one and two obtained by successive differentiation.)

The probability that any given person is left-handed is about 10%. Find the following probabilities: More than 3 out of 7 randomly selected people are left-handed___________

Identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) 4, 2, 0, -2, -4, ____