learly justify answer. lim (3x – 6) sin X -2 В.

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: tan (xy) lim = ? (х., у) -(1.0) у+ 2ху (b) - (e) (c) 3 (d) - 4 (a) 0 (e) 1

A:

Q: x łan 5x sin? (2x) lim

A:

Q: Find the exact value of x. 45° 100 Lim (O [0] 7h 15 VI UC

A: The sine of an angle is the length of the side opposite the angle divided by the length of the…

Q: Q3/ Solve the following. Choose two only. 1. lim x lnx³ X-0 2. lim x sin(1/x) 818 ex+2x 3. lim 818…

A: According to the question, we will calculate the limits of any two subparts.

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: Which of the following corresponds to the x-4 √x-2 evaluated? 0 4 2 DNE limx→4 ( when

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: QUESTION 5 lim f(x.y). Find (K)- (0,0) Let f(x.y)= O b.1 OC. -1 O d.1/2 e. Does not exist.

A:

Q: lim Σf (xf) Δx)]. V Axi→.

A:

Q: lim xy - 2y =? T,y)→(2,0) x2 + y? – 4x + 4

A: We have to evaluate the following limits -  lim(x,y)→(2,0) xy - 2yx2 + y2 - 4x + 4

Q: e2t - e-2 – 4t lim- t- sint

A:

Q: lim Sin (X+lTly)! X-T/4

A: If limit is not an any indeterminate form then put the values directly.

Q: ах? + bху + су? y-0 dx + exy + fyx“ ax? + bxy + cy 2. Evaluate lim lim- – lim lim y-0 x0 dx +exy +…

A:

Q: Find the limit

A: Here the given limit

Q: a, = V 2n + 6" %3D lim an %3D

A: Given: an=2n+6nn The main objective is to find limn→∞an

Q: tan (xy) = ? lim (х, у) ->(1,0) у + 2хy

A:

Q: x²+x y-2y lim (x,y)→(4,16) x- Jy

A:

Q: t t→0 et (c) lim = 1 True False

A:

Q: tan( xy) lim = ? 2. (х.у) -> (0,1) х*у+х (c) (с) 3 (d) - (е) 1 (а) 0 (b)

A: Limit is the value of the expression as the independent variable approaches certain value, not…

Q: Find lim, 3 3 z-81 4 z-3 18 O81 O None 118

A: in first part we use the integration of xn=xn+1/(n+1).  2nd part related to limit. see 2nd and 3rd…

Q: az? + sin? Let a be a nonzero constant such that a + 88. Let f(x, y) = and let L = limzv)-(0.0) f(x,…

A:

Q: (iv) Find lim r 2ª – x² sin

A: Limits

Q: x²+3x (t – 1)e' dt 2л — 4 - lim x→2

A: Given limit is : limx→2∫10x2+3xt-1etdt2x-4dt To find the value of limit by using L’Hospital’s.

Q: 8x+4-4cos?x+tanx Q1) Find lim X-0 4sin2x

A:

Q: Find lim x → 0 e* + 1 x² + 4 Answer only please (NB * is x )

A:

Q: Q5:The value of: * sin (5x) lim I-0

A: We have to find the value

Q: Evaluate cot x – cos x lim z¬7/2 (T – 2æ)°

A:

Q: a" +b" V lim /x AND= Vab tan x fii lim Anao e 2.

A: Given: iv)limx→0ax+bx21x iii)limx→0tanxx13

Q: e? – 1 – z lim 2 z-0

A: The given problem is: limz→0ez-1-zz2

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

A:

Q: tan(xy) = ? 2. (х.у) -> (0,1) х*у+х lim (a) 0 (b) (e) (c) (d) - (e) 1 3 -14

A: L'Hospital's Rule: If you have a some function f(x) or g(x) that both approach 0 as x→c…

Q: x?+2x If f (x): Solve to find lim f(x)? X-2 %D Vx+6-2'

A: The given function is: fx=x2+2xx+6-2 Solving the function for limx→-2fx Firstly direct putting the…

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: tan (xy) lim ? (х, у) ->(1,0) у + 2хy (a) 0 (d) - (b) (e) 1 - |3

A:

Q: (c) lim r³/x² 3/22

A: We have to find the limit value by using L'Hospital rule.

Q: Q27. The value of lim x-0 (1+x)5-e5x+sin x² x2 is? →

A:

Q: x+1 If f(x) = Solve to find lim f(x)? %3D Vx2+5-x'

A: Here is complete computation for your limit

Q: lim (sec' x- tanx) O T/2 00

A: We have to find the value of given limit: limx→π2sec3 x-tan3 x We know that sec x=1cos xtan x=sin…

Q: V1+ f(z) 42. Given that lim 1, then /1+ s(3z) lim A. V31 В. 31 C. D.

A:

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: D Find lim X,Y)→ (5,1) XY X+y or show it DNE.

A: We have to find limit

Q: If f(x) = 3 x2 +x , then f'(1+h) –f'(1) is limn→0 h DNE none

A: We can calculate as per given question

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

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: sin' 2x d) lim- x-0 sin' 3x

A:

Q: sin(x²-11x+30) Find limx→6 х-6 a. 0 b. 1 с. 7 d. 11 e. None of the above

A:

Q: tan(хy) = ? x²y (х, у) -> (0.1) х*у+х ¯y+x lim

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.