Math problem due today at 7 pm

Remember to use the Academic Support resources available on your homepage in Brightspace or or in the learning modules. Question 1: (6 points) Find two numbers with dif ference and whose product is a minimum.   Enter your answers in increasing order .

  First number: ____________   Second Number: ____________   Show your work and explain, in your own words, how you arrived at your answers.

__________   Question 2: (3 points) A farmer wants to fence a rectangular area of square feet next to a river. Find the length and width of the rectangle which uses the least amount of fencing if no fencing is needed along the river . Assume the length of the fence runs parallel to the river.

  Length:  ____________ feet       Width:  ____________ feet 68 392 10/9/21, 3:50 AM Southern New Hampshire University - https://snhu.mobius.cloud/modules/unproctoredTest.Print 2/5 Question 3: (6 points) Find the limit. Use l'Hôpital's Rule if appropriate.

  To enter  , type in    __________   Show your work and explain, in your own words, how you arrived at your answer .

__________   Question 4: (3 points) Find the limit using l'Hôpital's Rule.

  Enter an exact numeric value.

   ____________ Question 5: (4 points) Find the limit. Use l'Hôpital's Rule if appropriate.

  To enter  , type in    __________ ∞ ( − ) = lim x→ 0+ 1 x5 1 x7 = lim x→ 0 ta n (4x) x ∞ ln (x)= lim x→ 0+ 2x−− √ 10/9/21, 3:50 AM Southern New Hampshire University - https://snhu.mobius.cloud/modules/unproctoredTest.Print 3/5 Question 6: (3 points) Find an antiderivative of  in the variable  where  .   Remember to include a "+ C" if appropriate.

  Antiderivative = __________   Question 7: (6 points) Find an antiderivative with and .   Remember to include a "+ C" if appropriate.

   __________   Show your work and explain, in your own words, how you arrived at your answer .

__________   Question 8: (4 points) Find the inde ) on the domain of positive real numbers.   Remember to include a "+ C" if appropriate.

  Enclose arguments of functions in parentheses. For example,  . To enter  , type sqrt(a).    __________ 5 − 7 x3 x5 x6 x x ≠ 0 F (x) (x)= f (x)= 4 + 24 + 18 F ′ x3 x5 F (1)= 0 F (x)= x > 0 sin (2x) a−− √ ∫ ( − ) dx = 6 x 1 4 13 x−− √ 10/9/21, 3:50 AM Southern New Hampshire University - https://snhu.mobius.cloud/modules/unproctoredTest.Print 4/5 Question 9: (3 points) Find the inde   Remember to include a "+ C" if appropriate.

  Include a multiplication sign between functions. For example,  * ..    __________   Question 10: (4 points) Find the inde   Remember to include a "+ C" if appropriate.

  Enclose arguments of functions in parentheses. For example,  .

   __________ t et ∫ 4 dt= et sin (2x) ∫ ( − 7sin (x)) dx = x 1 1 3 10/9/21, 3:50 AM Southern New Hampshire University - https://snhu.mobius.cloud/modules/unproctoredTest.Print 5/5 Question 11: (4 points) (a) Estimate the area under the graph of the function from to using a Riemann sum with  subintervals and right endpoints.

  Round your answer to four decimal places.

  area ____________   (b) Estimate the area under the graph of the function from to using a Riemann sum with  subintervals and left endpoints.

  Round your answer to four decimal places.

  area ____________     Question 12: (4 points) Estimate the area under the graph of the function from to using a Riemann sum with  subintervals and midpoints.

  Round your answer to four decimal places.

  area   ____________     f (x)= 1 x+ 4 x = 0 x = 2 n = 10 = f (x)= 1 x+ 4 x = 0 x = 2 n = 10 = f (x)= x + 5 − − −− √ x = − 2 x = 2 n = 10 =