Question 3 For Iunctions that are positive as → 0 we say J grows Jaster than g as x → 0 1I f (x) lim = 00. x→o g(x) This is the same as if g(x) lim = 0, x→∞ f(x) and in words we could also say g grows more slowly than f as x → o. For each pair of functions below, use limits to determine which function grows faster as x → o. Show all work. (a) In(x) and ln(2x) (b) eª and 22æ (c) eª and eª–1 (d) eª and x52" (e) ln(e" + cos x) and x In(x)

Q: Mark each statement as true or false. a.) If a function is differentiable at x=3, it must be…

A: Topic = Application of Derivative

Q: 2. Subtract f(x) from f(x+h).

A:

Q: (Pls don’t use the L-hospital rule) Need help with this problem step by step. Thanks

A: Answer and explanation is given below..

Q: 32? And are

A: {x2                               if x<-2f(x)={x1/5                           if…

Q: Let j(x) 1 Calculate j' (3). %3D 8 x+2 Answer): j' (3) =|

A:

Q: Use the limit of the difference quotient definition to find the derivative, f'(x) must show the…

A:

Q: en limf(x) =f(c). TH

A: a)  For a function f(x), limx→c f(x)=f(c) means that the function is continuous at x=c.  In this…

Q: Which of following limits is the derivative of g(x) =5x at =2? 10 – 5h lim h 10 + 5h lim h>0 h 10 +…

A:

Q: W 9 O(A) and ronl Graph of f' 38. The graph of f', the derivative of f, is shown in the figure…

A: Given information:The graph of the function shown below is of  where  is the derivative of .To…

Q: Find the derivative of the function by the limit process. F(x)= 7/x2    To solve we use the…

A:

Q: f(x) - f(a) 15. Use the alternate definition lim x-a of change of f(x) at the given point or value…

A: I have explained everything with in the solution. Please go through that.

Q: Cannot solve

A: If r= (x,y) Here , x= -8 , y=9

Q: 4. Explain what each of the following items tell you about the graph of f(x) using vocabulary such…

A: the given criteria for the function f is: f0=3f'3=1limx→∞f(x)=10f'(x)>0 for all x.f''(x)>0…