use the pathstest to show that the limit Dres wot Exist Fexiy) = e_I

Q: Evaluate lim f(x), lim f(x), and lim f(x) at the point a = 5, if the limits exist. (If an answer…

A: Given function : f(x) = 10 -x  if x ≤5 f(x) = x + 3 if x > 5

Q: The limit as x goes to zero of x-1 exists.   True or False?

A: We need to say whether the given statement, “The limit as x goes to zero of x-1 exists.” is true or…

Q: the limit cannot be zero for part b?

A:

Q: find its limit.

A:

Q: How does the sandwich theorem enable us to calculate a variety of limits?

A: Sandwich theorem: Consider 3 function f(x),gx,hx such that fx≤gx≤hx. Also, assume that limx→cf(x)=L…

Q: lim x++∞ x² + x e²x + Inx

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: lim f(x) given that |f(x)/x² + 1|< 1 x→+∞

A: Recall: Squeeze Theorem for limits:              Assume that functions f,g and h satisfy…

Q: y z lim (x,y,z)>(0,0,0) x² +4y² +9z .2

A: Given limit, limx,y,z→0,0,0yzx2+4y2+9z2

Q: I can't find the limit.

A: Obtain the value of limit as follows:

Q: Use two different paths to demonstrate that the limit: lim(7,9)→(0,0) x*y?+(x=y)?

A:

Q: 2x x→∞ 3x² +5 3x xx√√√x² x² +4 X lim x→→∞ 2 sin î (a) lim (b) lim (c)

A: Given

Q: 23) lim f(x) x→1- f(x) 5- 4+ 3+ 2+ -5 -4 -3 -2 -1 -1. 5 х 2 4 -2+ -3+ -4+

A:

Q: lim ) (sinx\ 1-cosx X→0

A:

Q: X- Zx +3x+2 lim

A: Solution of question as follows

Q: 8. Evaluate the limit by using a change of variable. 1 X6 1 d. lim x→l_x³ Vx 2 x4 √x³ - 8 e. lim 1…

A:

Q: Use the definition of the limit of a function of two variables to verify the limit.

A: Verify the limit limx,y→a,by=b

Q: lim, (V+x+1 - V+1) – Vx² x* + 1

A:

Q: lim x3 In(x) X→0+ to

A:

Q: (x+2)7(x-5)* lim x→b (x+6)3 (x+8)10 DNE %D

A:

Q: 3r+ |エ lím ー0 7r -5|r

A: Given : limx→03x+x7x-5x