4 1. lim X→0 x² 2 1-cosx

Q: II. INDETERMINATE FORMS COS X X 5. lim x →∞0

A:

Q: 1. Determine if the following limits exist: 1² + y? (a) lim (1,y)→(0,0) e² +y² – 1 12 sin(y) (b) lim…

A: In the question we have to find limit.

Q: Q2/ a) If f) = , what are the domain of f(x) and g(x)? sin 6x lim 0 sin 9x b) Find

A:

Q: a. limr→0 cos(x) b. limx→n

A:

Q: - 1 X If lim ([sin ¹x] + [2²sin ¹' (2x)] + [3³ sin-¹ (30)] x →0 X X + [x²³sin-¹ (x2x)]) + ... +…

A:

Q: Use l'Hôpital's rule to find the limits 20 - T 30 + T 17. lim /2 cos (2T - 8) 18. lim 0--1/3 sin (0…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 4 35₂ In evaluating 2 dx X√√x²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

A: We have to find the value of f(x) at x= 2.9.

Q: 3r + cos r 2. Use Squeeze Theorem to evaluate_ lim 1-00 V1 +r2 - 5x

A:

Q: пу-1 TT 6. lim y→0_2y² + y(e2™y-1)

A: Indeterminate Forms: The symbols like 00, ∞∞, 0·∞, ∞-∞ are called indeterminate forms L'Hospital's…

Q: Show necessary computation x²-9y? lim (x,y)→(1,0) tan-1 (x4 – 4xy + y²) lim (х,у)-(0,0) х-Зу b. а.…

A:

Q: A. MCQS: I. LIMITS (2x+7x+6 3x2+5x-2. 1. lim-2 ( - 2. lim,-2 x+2 A.0 B. C.D. co A. 0 B. 4 C. 12 D.…

A:

Q: Q3// Evaluate (a) lim,4 VE-2 S-V49 sin 3y cot 5y (b) limy-o y cot 4y

A:

Q: 2 i (z-i) lim z?+1 1 -1 о 2i

A: 1 Just use L'Hospitals rule.

Q: の lim 3x? メ→ 1-cos (x) b) lim 6) Xうo

A:

Q: 1 – cos(xy) - lim (x,3) → (0,0) x²y²( – 9 + y) Evaluate Use DNE for does not exist, oo for infinity…

A:

Q: 1. Solve the following limits. (a) lim II 1+ r? x In x (b) lim 2+ sec (3x) (c) lim /6 tan (3r)- 1

A:

Q: 1- sin r 6. Find lim 1/2 CSC x Csc x

A:

Q: 2) Use the figure to give approximate values for the following (if they exist). Enter your answer as…

A: The above figure shows the graph of function f(x), find the following: (a) f(1)(b) lim f(x)x→1(c)…

Q: 1 1 4. lim X→0 In(1+x) Arctanx

A: 4.

Q: 2y-n -Tt 7. lim cos y 2

A: Given:         limy→12π2y-πcos y    Let   π2-x=y, ⇒π-2x=2y      As y→π2,x→0

Q: x² – 9 16. lim x - - 3- x +3 (4 + h)² – 16 18. lim h→0 sin²x 20. lim htan³x 4

A:

Q: tan (xy) lim = ? (х, у) ->(1,0) у+ 2ху 1 1 (b) (e) (c) 를 (d) i (а) 0 (e) 1 3 ||

A:

Q: Q3. Compute the following limits if they exist. sec a - 1 (a) lim x – sin r (b) lim 20 x - tan r 2 –…

A: Q.3 part a) Substituting the limit in function, This is indeterminate form 0/0,

Q: 2a? sin(y) lim (x ,y) → (0,0) 2x2 + 4y2 Evaluate Use DNE for does not exist, oo for infinity or -00…

A: Given limit, lim(x,y)→(0,0)2x2sin(y)2x2+4y2

Q: 8 sin (1r) 3. Find lim 5.r

A: In the question we have to find lim x→08sin(4x)5x

Q: Find the limits: Vx + 25 – 5 (а) lim т? + 5х + 1 (b) lim x→2 x3 – x – 1 1– sin 0 (c) lim 05 1+…

A:

Q: Along the path x = e y +6xy find lim (x.y)→(1,0) 3x-y-3 Along the path x = e y? +6xy ind lim…

A: Let's find.

Q: 2 dx 5, is same as evaluating lim cos C+2+ F(<x))". Determine the value of f(x) if x=3.22 In…

A:

Q: tan(xy) = ? lim .2. (х.у) >(0,1) х*у+x 1 1 (b) 1 (e) (d) - (а) 0 (e) 1 4 - |3

A:

Q: Q2: Evaluate: [1] 21 lim m COSXVI+ COSX – v1-x, sin-1(x) V1+x - [3] lim-o

A: Limit of a function determines the continuity of a function. Three types of limits exist, one is…

Q: xsinx lim X→0 ex+e¯x-2cosx

A: To find the value of the limit, substitute the limit value for x in the given expression and…

Q: V3r-1 7. lim X- sin? x-cos(2x)

A:

Q: tan ( xy) lim 2. (x,y)→(0,1) x´y+ x (a) 0 (b) (c) (d) (e) 1 -/4 -3 || -12

A: This question is related to Differential Equations.

Q: f(x) Consider the function: 9 sec z 18--7 tan x 9(x) What is lim f(x). I 9(x) -? Note: For limits at…

A: I have given this answer in step-2.

Q: tim Q2 Find the limits liw h +h cosh 1- Sinh.cosh 2-lim 2x-8

A: Limit value of the rational function

Q: - Using any results from the course material, find the following limits: sin(x? – 9) а. lim x-3 (x2…

A: Solution:-

Q: I. Evaluate the following limits. sinh r2 → r2 1. lim z→0 sinhr 1

A: We will apply DL hospital rule more than once to solve this question.

Q: - Find lim Re(2) [Hint: use z = x + iy.] z -1- i - Find lim 2+1+i 22 – 2z + 2

A:

Q: tan ( xy) :? lim (х.,у) -> (0,1) х-y+x 1 (e) (d) - (а) 0 (b) 2 (е) 1 4

A:

Q: Q:Evaluate the following limits. (1) lim cos a)" +(sina)" -1 ',xe(0, Tt/2) x--2 X-2 (ii)lim cos a)"…

A: (i)      limx→2cosαx+sinαx-1x-2If we put x=2 in the limit, we get 00 indeterminent form.Therefore ,…

Q: 14.6.9. Show that lim sin(a? + y²) dA(x, y) = |æ|,]y|<n I sin(a? + y?) dA(x, y) = 0. lim %3D…

A:

Q: L’Hôpital’s Rule for ∞ /∞ Evaluate the following limits.

A: Part (a): Given, limx→∞4x3-6x2+12x3-10x+3

Q: sin2z+721任22 4. lim よー2 z (2十1)

A:

Q: 3. Compute the following limits. Justify your steps. 2t sin(x – 1) (а) lim t→0 tant (b) lim I→1 x2 –…

A: Answer of (a). 2 (b). 1/2

Q: ax? + sin? Let a be a nonzero constant such that a + 27. Let f(x, y) and let L lim(z,y) >(0,0) f(x,…

A:

Q: t2 – 1 2. lim t-2 t² + 3t – 1

A: Evaluate: limt→-2t2-1t2+3t-1 Substitute t=-2 . limt→-2t2-1t2+3t-1=-22-1-22+3-2-1

Q: 1-sin /r'y| If the inequality * (0,0) 24

A:

Q: Q.1 Determine a, b, c, d & e such that cos ax + bx+ cx + dx + e 2 lim-

A: To find the values of a,b,c,d and e

Q: Show that (x + 1)² sin y lim (x,y)→(−1,0) (x+1)4 + y² does not exist.

A:

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.