(ii) lim cot(4x) tan(3r) .() ledo d (iii) lim 3. 1+

Q: Cos x-1 2- Show that lim = 0

A: We have to find the limit of the given expression. this can be done as follows:

Q: Cos Q1:solve lim オ→+0 π

A: Step:1     Solve:limx→∞  cosπxπx

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

A:

Q: sin 04) find limx-2n 2x-4n S0 (x²+x+1)* Q5) lim- (r²+1)100

A: In the given question we have to find the limit of the question 4 and question 5. the question 4 is…

Q: x łan 5x sin? (2x) lim

A:

Q: 2x - 6x 34. lim x-0 sin 2x 35. lim 2 1- cos 2

A:

Q: Find the limit

A: We first separate the limits

Q: cos(²²) – 1 ()- lim 7 x3

A: Given that, limx→0cos(x2)-17x3 By using limx→0cf(x)=climx→0f(x), where c is constant.…

Q: sin?x-1 10. lim sinx-1 2

A: Let f,g be functions which are continuous and differentiable. If while computing the limit…

Q: Rx+2sinx Q2.a) lim sin (). sec (in 3+x

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. x² tan( + 47) + 2 tan-1x lim =? (a) 1 (b) -2 (c) -1 (d) (e)

A:

Q: sin(1 – t) |2 – 2t| (b) [8 marks] lim t+1-

A: this is left hand limit then limit approaches from left side

Q: Q1: Solve Two Only : x sin (x+sinx)" a- limx-0 sin'x b-lim0 X-xcos4x

A: Solve any two

Q: 1- cos 5x lim x? 2 x→0 а. -2.5 b. -12.5 С. 12.5 d. 2.5

A:

Q: -2x lim (e cOs x) х) x → 00

A:

Q: (cos 0 -1) 4. lim 5. lim sec(20 + n)

A:

Q: b) lim, . sin(8z)

A:

Q: b→-∞ J tan- ((b+3)/4) None of these tan (3/4) d0 lim b→-∞ tan-! ((b+3)/4) sec- (3/4) do b→-…

A:

Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO FO x-5 • lim х-5 х2-25 = 10 FO

A:

Q: cos 5x Find lim ( x³ + 10,000 x→0

A: We have to find the given limit: limx→0x3+cos 5x10, 000 This limit has determinate form so we just…

Q:

A:

Q: cos x2 - 1 2. Find lim→0 2x 81,341 123

A: Answer and explanation is given below

Q: (а) 1- cos 4x lim x? x-0 5-х (b) lim- 45 Vx-1-/2x-6 312 -t- 2 lim 1² -1 (с)

A:

Q: cos h -1 lim h

A:

Q: What is lim tan(x)? Why? AY 10 8 6. 4 2 -0.S 0.ST, 0.5n, 1.5a, 27 2.5m -4 -10

A: Given limit is limx→π2+tan(x) As shown in the graph of tan(x), as x approaches π2 from right side ,…

Q: cos(7x) – cos(9æ) lim x2

A:

Q: Q\ Find lim tan(x)cos(x) O 2 -1

A: The given limit is of the form ∞0 form. Let L=limx→π2-tan xcos x⇒ln L=ln limx→π2-tan xcos x…

Q: tan( xy) lim (х.у) >(0.1) х"у+x = ? 1 (b) 2 1 (c) 3 (a) 0 (e) 1

A:

Q: 1. 5.lim cos(x) sin(x)

A:

Q: Q:B/ Find lim, [tan x-sec x].

A:

Q: et - e* lim,0 2 sin x

A: Consider the given function, limx→0ex-e-x2sinx put the value of limit into the function,…

Q: 4. lim -0 A. -2/2 B. 1 C. 2 h D. Does not exist sin

A:

Q: cos(x) lim 2

A:

Q: (iv) Find lim r 2ª – x² sin

A: Limits

Q: 1-x c) lim- x1 1-Vx 121 sin x d) lim (Hint: Use a calculator to make a table.)

A: c) limx→11-x1-xd) limx→0sin xx

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

A: We have to find the value

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

A:

Q: cos x - 1 75. lim - x→0 sin? x tan-1

A:

Q: 1. Find lim an 3(x+h)-tan 3x A. 3 sec 3x tan 3x B. sec? 3x C. 3 tan 3x D. 3 sec2 3x

A: limh→0 tan3x+h-tan3xh So here fx =tan(3x) Now we need to find derivative of fx with respect to x…

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

A:

Q: (b) Find lim, 0 xª cos 2.

A:

Q: e* – 1 lim x-0 tan 2x

A: Given: limx→0ex-1tan2x

Q: -2x – 1 Find lim X+0 sin 3 sin()

A: Using formulae of limits

Q: r2 lim cos where k is - 00 - sec?! (A lim tan B lim - cos?- lim 2. 2.

A:

Q: 2x tan -1 I + COS (b) lim

A:

Q: 7. *Find the values of a and b lim sin(ax-2a) x-2 = 3 %3D x-2

A:

Q: 3+2r lim エ→0 =?

A: Given , limx→03x2+2xx

Q: x2/3 +x-1 lim x-00 x2/3 + cos? x

A: It is limit problem in which we can find the answer by applying given limit in the function.

Q: 10 sin(4x³) 12x8 lim X→0

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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.