prove a few more cases of the following general statement (there are so many possibilities that you should select just a few, if any, that interest you): If lim f(x) - lim g(x)- I and lim f'(x)/g'(x) - (), then lim f (x)/g(x) . H ) ere [ ] can be a or a+ or a or oo or -oo, and can be 0 or oo or -oo, and ( ) can be I or oo or -oo

Q: 1. If f(r) = , do the following: %3D iii) What is lim

A: Given Function, f(x)=1x

Q: If f(x) = (1+%) 3 ) 6x *", find lim f(x).

A: We have to find limx→∞fx when fx=1+3x6x If we put limit value then we get that it is 1∞ form We know…

Q: Prove that limxc f(x) = Lis equivalent to limxc [ f(x) − L] = 0.

A:

Q: f(x) +3 4+ -4 If lim 3e² 00 0-3 O-4 Oe-3 =e", then lim f(x) =

A:

Q: 3) If the lim f(x) = 2 and lim f(x) = -1 %3D x-3- x-3+ Then what is the lim f (x) = x→3 %3D a) Why?

A: To find the limit of the f(x) at x=3

Q: h(x)-h(1) 6. If h(x)=- J4-x² , evaluate lim x>1* x-1

A:

Q: Find the value of lim f(x) 1 f(x)3= 1+5/x -0.6 -0.5 0.16 01 E -0.6

A: To find out the correct answer.

Q: Example 13: lim x sin(é)

A: To find the limit (x tends to infinity) xsin(2/x)

Q: Why does this equal 11 and not 9?

A:

Q: If lim f(x)=-2 and lim g(x) = 2, what is the value of lim [f (x)+2g(x)]?

A: Given, limx→afx=-2  and  limx→agx=2

Q: Show that if lim f(x) = lim h(x) = 3, and if f(x) ≤ g(x) ≤h(x) for 2-0 x-0 all z € (-1,1), then lim…

A: Given that limx→0fx=limx→0hx=3 and fx≤gx≤hx for all x∈−1,1. We have to prove that limx→0gx=3.…

Q: Your friend from Calc 2 says that the following statement is not true: x2-x-2/x-2 = (x+1) She is…

A: We have to answer the given questions.

Q: 5. If lim f(x) = 8 but lim f(x) does not exist, what can you X+2+ X+2 say about lim f(x)? X2-

A: We know that, limx→afx=l, if: limx→a+fx=limx→a-fx=l

Q: FIf f(x) = { x² – 1, x 3 Find a) lim f(x) = b) lim f(x) = c) lim f(x) = x-1 x-3 d) lim f(x) = e) lim…

A: Given  f(x) = x2-1,x<3x+5,x≥3

Q: lim F(x),

A:

Q: 61. lim x¹/(1-x) x-1+

A: NOTE: Refresh your page if you can't see any equations. . use the exponent rule

Q: Can you help me solve this using L’Hôpital’s Rule?

A:

Q: if x1 then lim,-1 f(x) is 3 if x 1 (b) 3 3. Let f(x) = (a) 1 (c) not exist (d) other

A:

Q: Let n be a positive integer, and a 0 a constant. Use integration by parts to show that [x³eª² dx =…

A:

Q: x²-1 if x < -1 -2 if x ≥ - 1 lim g(x), where g(x) = x+1 x-

A: Steps:

Q: Question 2. Sketch the graph of a function f(x) defined for all x € R that satisfies all of the…

A: The graph is as follows

Q: If lim f(x) = L, then f(a) = L. X+ a A) True B) False

A: We have to check

Q: а) The function f is defined by 2, if x2 i) Find lim f(x). Give your reason.

A:

Q: Let's mix in some more interesting functions 3) lim X In(x) (hint: you may want to graph In(x) to…

A: Graph of y=ln(x):