I Need Help With These Questions please.

[shadowwalker]

• Please solve each question in the space provided. You should give the details of your solutions and not just the final results.
  
  Q−1:
  1. Find the domain of the function
     f(x)=4x−9−x2−36−−−−−−√fx=4x−9−x2−36
     .
  2. Let
     f(x)=3x−5 −−−−−−√fx=3x−5
     and
     g(x)=5x2−3gx=5x2−3
     . Find
     (f∘g)(x)(f∘g)(x)
     and
     (g∘f)(x)(g∘f)(x)
     , simplify your answers.
  
  Page Break
  Q−2:
  1. Solve for
     xx
     :
     1−8ln(2x−17)=141−8ln⁡2x−17=14
     .
  2. Find the slope of the tangent line to the following curve at the designated point:
  
  y4−4y2=x4−9x2, (3,2)y4−4y2=x4−9x2, 3,2
  .
  
  
  Page Break
  Q−3: Use the definition of the derivative to find the derivative of the function
  f(x)=1−9x−−−−−√.fx=1−9x.
  
  
  Page Break
  Q−4: Find
  f''(x)f′′(x)
  for:
  1. 
     f(x)=lnx4xfx=ln⁡x4x
     .
  2. 
     f(x)=2e−x2fx=2e−x2
     .
  Page Break
  Q−5: Find the points at which
  f(x)=(x−2)4(x+1)3fx=(x−2)4(x+1)3
  has relative extrema.
  
  
  Page Break
  Q−6: Determine the area of the largest rectangle that can be inscribed in a circle of radius 1.
  Page Break
  Q−7: Let
  f(x)=ln5x2+4x2+1fx=ln⁡5x2+4x2+1
  . Find the intervals on which
  ff
  is increasing or decreasing.
  
  Page Break
  Q−8: [3+2 marks]  
  1. Use the logarithmic differentiation to differentiate the function
  
  f(x)=x4(x−2)(x2−2)(2x+3)−−−−−−−−−−−−−−√3f(x)=x4(x−2)(x2−2)(2x+3)3
  .
  1. Find an equation of the tangent line to graph of
     f(x)=lnxlog2xfx=ln⁡xlog2⁡x
     at
     x=2x=2
     .

 

[Deleted member 4993]

Link

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[R.M.]

Question 1: to find a domain, ask yourself "what CAN'T I plug in for x?" Also, clean up your formatting. Does "x2" mean x squared, or x times 2? For exponents, ^ is your friend.

 

[Dr.Peterson]

• Please solve each question in the space provided. You should give the details of your solutions and not just the final results.
  
  Q−1:
  1. Find the domain of the function
     f(x)=4x−9−x2−36−−−−−−√fx=4x−9−x2−36
     .
  2. Let
     f(x)=3x−5 −−−−−−√fx=3x−5
     and
     g(x)=5x2−3gx=5x2−3
     . Find
     (f∘g)(x)(f∘g)(x)
     and
     (g∘f)(x)(g∘f)(x)
     , simplify your answers.
  
  Page Break
  Q−2:
  1. Solve for
     xx
     :
     1−8ln(2x−17)=141−8ln⁡2x−17=14
     .
  2. Find the slope of the tangent line to the following curve at the designated point:
  
  y4−4y2=x4−9x2, (3,2)y4−4y2=x4−9x2, 3,2
  .
  
  
  Page Break
  Q−3: Use the definition of the derivative to find the derivative of the function
  f(x)=1−9x−−−−−√.fx=1−9x.
  
  
  Page Break
  Q−4: Find
  f''(x)f′′(x)
  for:
  1. 
     f(x)=lnx4xfx=ln⁡x4x
     .
  2. 
     f(x)=2e−x2fx=2e−x2
     .
  Page Break
  Q−5: Find the points at which
  f(x)=(x−2)4(x+1)3fx=(x−2)4(x+1)3
  has relative extrema.
  
  
  Page Break
  Q−6: Determine the area of the largest rectangle that can be inscribed in a circle of radius 1.
  Page Break
  Q−7: Let
  f(x)=ln5x2+4x2+1fx=ln⁡5x2+4x2+1
  . Find the intervals on which
  ff
  is increasing or decreasing.
  
  Page Break
  Q−8: [3+2 marks]  
  1. Use the logarithmic differentiation to differentiate the function
  
  f(x)=x4(x−2)(x2−2)(2x+3)−−−−−−−−−−−−−−√3f(x)=x4(x−2)(x2−2)(2x+3)3
  .
  1. Find an equation of the tangent line to graph of
     f(x)=lnxlog2xfx=ln⁡xlog2⁡x
     at
     x=2x=2
     .

It looks like you pasted from a source that provides duplicate formats for each expression, and didn't even look at the results. Either fix that, or type it in by hand, or attach an image.

But don't bother unless you're willing to do some work. We don't take tests for you.

 

[mmm4444bot]

Moderator Note: The OP had subsequently replaced their text with a link, but the link was broken. (Error message: "Sorry, access to this document has been removed. Please contact the person who shared it with you.") Hence, I reverted the op back to the original text. OP has been notified.

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[imath]\;[/imath]