2. Given f(x)= a) 0 [x+1 ifx<0 x-1 if x20' b) 1 , find lim f(x) if it exists. X-0 c)-1 d) it does not exist e) 2x

Q: tan 3x lim x→0 \ e2x – 1 3/2 O 1/2 O 2 O 2/3

A: Solution:GivenTo find the limit oflimx→0 tan 3xe2x-1=?Formula:ddxeax=aeaxddx tan ax=asec2 ax

Q: 22. If f(2)=sin 2, then lim (2)-f(z) z-2 2-2m (A)-2T (B)-1 (C) I (D) 2T

A:

Q: Let f(z) 2 = = (-)². Show that lim f(z) does not exist. z➡0

A:

Q: I am trying to figure out the answer to this problem using L'Hopital's rule. please show all steps.…

A: Given,           limx→02xx+3-3

Q: 3. lim,10 Vx – 1

A: The limit of any function is defined for any function F(x) on any interval that contains point at…

Q: Suppose lim f1x2 xSa o and lim glx2 = ". Prove that xSa %3D lim 1f1x2 + glx22 xSa

A:

Q: A) Vx2 +8-3 lim x-1 x+1

A: By using l'Hospital's rule we solve the given problem as follows :

Q: 1. Complete the following based on the graph of f(x). 0 10-8-6-4-2 CO 6 4 2 2 -4 क -8. f(x) e 246 6…

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: 2f(x)=x² x-1 f(x)+1 3. If lim f(x) = 2, what is the value of lim a) 0 b) 1 ? c) 2 d)

A: Given: Limit ( x-&gt; 1) f(x) = 2  Need to find- Limit ( x-&gt; 1) [ 2f(x) - x2 / f(x) + 1 ]

Q: tan(3x) lim x→0 2x2 + 4x

A:

Q: flx) = Jx-7 Lim f(3+h)-f(3) ||

A:

Q: If V5 – 2x? < f(x) < V5 – x? for -1 <x < 1, find lim,-o f(x).

A: Given  5-2x2 ≤ f(x) ≤ 5-x2 for  -1≤x≤1.

Q: . The function f (x) is defined by the rule 2-36 if x + 6 f (x) x-6 25 if x = 6 (a) Calculate lim f…

A: Continuity criteria :  f ( x ) is continuous at x = a when following properties are satisfied :  1)…

Q: 2. Evaluate lim,.

A: (1) Consider the provided limit, limx→91x-191x-9 Find the limit of the above expression. Simplify…

Q: The function f is continuous for all real numbers. If lim f(x) = 0, then what is lim xe-2x)? x-2 x-1

A: The function f is continuous for all real numbers  If limx→2f(x)=0then if we put x=2t then…

Q: Let A.=(-11.1- and B. 4. for all n E N. 1. PL lim PL(A) 2 BUB. =2 3. AL lim u(A.) -3.

A:

Q: I if X > 4 and J (X). 4X + 1 i1 X<4. Find lim f(x) x→4+

A: Given; f(x)=√x-1 if x&gt;4 and f(x)=x2-4x+1 if x&lt;4.

Q: 31. If f is continuous and f(3) = 9, which of the following statements must be true? (A) lim f(3x) =…

A: Here we define which statement is true or false.

Q: If 4æ – 11y = 5 is the tangent to f(x) f(x) - f(3) at a = 3, then lim | (A) =! (B) 규 (C) 4 (D) (E) 4…

A:

Q: In (2-x) 1-x²-y2¹ (a). Find and sketch the domain of f. 1. Given function f(x, y) = ,do the…

A:

Q: Let f(x) = x² - 4x-21 X-7 Find a) lim f(x), b) lim f(x), and c) lim f(x). X→7 X-0 X→-3

A:

Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: Use the limit definition of the derivative to determine f '(2) if gnibnoqonos su snimals (T ni 4 =…

A:

Q: 5. Calculate lim f(x), where x+1+ f(x) = = its 12.05 (c)-2 (d) 2 (e) does not exist 5A 5B if x 1 x-1…

A:

Q: (a) Lim X–1 x +1 -2 X

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: (A) (B) ƒ(5) - ƒ(3) 5-3 f(3 +h)-f(3) h (C) lim h→0 || f(3+h)-f(3) h

A:

Q: x²-49 X-7x²-7x 2. Evaluate lim: 3. Evaluate lim √x+1-3 X-8 x-8

A:

Q: Suppose f is a function that satisfies the equation f(x + y) = f(x) + f(y) + x2y + xy2 for all real…

A:

Q: 12. Let L = lim a>0. If L is finite, the (A) a=1 (B) a=2 (C)L- (D) L-

A: We are asked to find a value and L values.

Q: x) = (V5x – 1, 2х, X = 1 x> 1

A: A function f(x)f(x) is said to be continuous at x=a if x→alimf(x)=f(a) A function is said to be…

Q: In(2+x) lim, x+-1 X+1

A: