 # In exercises 1-4, find each limit. Show intermediate steps. x2-4 ...

## Question

Show transcribed text

## Transcribed Text

In exercises 1-4, find each limit. Show intermediate steps. x2-4 - 1. lim x-*2 X2 + 5x-14 - 3x - 5x² 2. lim 2x² +4 3x 3. lim x 5+ 5 - X 4x - 9 4. lim x-&gt; m x + 3 3x + 1 5. Find the equation of the line that is perpendicular to the tangent line to the curve, y= at the point (1,2). 4x - 2 In exercises 6-10, find the derivative of each function. Simplify your result in exercises 7 and 9. 6. y=sin53x = 7. V = e³* (3sin X - cosx) 8. Y = (x + 2) (xx + 3) 9. Y =x2x = 10. y = = sin" (3x) + In xsec X 11. Given (x) - After sketching a graph a. Find the local maximum and minimum values of f b. For which values of X is f concave upward? 12. A box with a square base is to have an open top. The area of the material in the box is to be 60 sq in. What should the dimensions be in order to make the volume as large as possible? 13. A 10-foot ladder is leaning against a wall. If a person pulls the base of the ladder away from the wall at the rate of 1 foot per second, how fast is the top going down the wall when the base of the ladder is 6 feet from the wall? In exercises 14-17, evaluate the integral. 14. x² 2 + x 3 dx 15. / cos³ X sin X dx (lnx)³ 16. dx 2 17. / x x - 1 dx 1 18. Find the area enclosed by the curves y=x2-2x - and y = =2x-x² 19. The region bounded by the parabola y=x², = the line X = 1, and the x-axis is rotated about the y-axis. Find the volume of the resulting solid. 20. A bacteria culture starts with 300 bacteria and after 3 hours there are 600 bacteria. Assume that the bacteria grow at a rate proportional to their size, which means you can use the function, y = Ae where Y is the number of bacteria and t is time in hours. a. Find the number of bacteria after 5 hours. b. When will the population reach 2,000?

## Solution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

By purchasing this solution you'll be able to access the following files:
Solution.pdf.

\$50.00
for this solution

or FREE if you
register a new account!

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

### Find A Tutor

View available Calculus Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.