tan (xy) lim = ? (x.y)→(1,0) y+xy (c) 3 (d) - (e) 1 (a) 0 (b) 114

Q: Evaluate the following limits: 1-cos¹(x) (i) lim zsin(2x) (ii) lim In (√) +1 2²-1 (iii) lim sin(x) -…

A: Given :limx→01-cos4(x)sin(2x)lim x→1 lnxx2-1lim x→π4 sinx-22cosx-22lim x→01+tan(2x)1x

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: X-3 lim y→3+ Vx2¬-9 х2-9

A: Find the limit of limx→3+x-3x2-9

Q: (c) lim →1 是 æ-1 1 T-1 = 3.

A:

Q: 9 (y) -1.0% DNE [y²+5 ify<-2 1-3y if y2-2V lim g (y) lim 9 (y) (a) lim g (y) 1-3y if y2-2. 17 (b)…

A:

Q: Show that x²y + x² lim (x,y) →(0,-1) 24+ (y + 1)² does not exist.

A:

Q: What is lim f(z) z→1 9(2) given f(x) = e2" and g(x) 3x2 – 3x + 6 ?

A:

Q: If f(x)= 2x² +1, then lim S(x)– f(0) is (A) 0 (B) 1 (C) 2 (D) 4 (E) nonexistent OB OD O C O E O A…

A:

Q: f(3+ h) – f(3) (4) 7. For f(r) = x² – 4x + 5, determine lim h0 h (6) 8. Consider the curve defined…

A:

Q: f(x)=√x −7 lim h→0 f(6+h)−f(6)/h

A: Question is solved.

Q: For the function f(x) = 4x² + 15x + 35, find f(x + h) – f(x) f'(x) using the definition lim h 0 h O…

A: We will use the definition and then use the limit of h goes to 0 to find the derivative of the…

Q: пу-1 lim y→0_2y² y(e2™y–1)

A: To evaluate limy→0(πy(e2πy−1)+πy−12y2) Rewrite the given expression:…

Q: lim (4+ (2? + y°) In(x² + y²)) (1,y)(0,0)

A: Given; lim(x,y)=(0,0)[4+(x2+y2)ln(x2+y2)]

Q: (A) f(x) = √√√x + 2x (B) f(x) = √√√x – 2x² (C) f(x) = 2x² + √x (D) f(x) = 2x − √√x

A:

Q: Find lim v² + 2x – x. (а) 0 (b) 1 (c) 2 (d) o (e) DNE

A:

Q: Q2. Find the x² + y² lim (x, y)→(0, 0) √√x² + y² + 1 − 1

A: We have to solve above question and find  limit

Q: f" (h+x)-j" (x) li h→0

A:

Q: (2e + 1)" lim (tan(x))" DNE ||

A:

Q: x° +2y² +x*y lim (* ,y') → (0, 0) x* +3y - x*y

A:

Q: consider the following function: f(x)=cos(2-2x)

A: The given function .The aim is to find the period of the function.

Q: Why is limx→0(cos(x2))=0 but limx→0(cos(x-2)) is not defined?

A: We have to show  but  doesnot existNote: It is given  which is incorrect,  is correct

Q: e3x + 5e* (с) lim x→0 7e3x – Te™

A: We have to evaluate the given limit.

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: (a) (b) x + y f(x, y) = √√x+y f(x, y) = sin (x+y) √√²-1

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.