cos x In (1 + x) a) dx. b) lim 1 - cos x

Q: acosx+bx sinx-5 (ii) Find the values of a and b so that lim exists and finite

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

Q: 2. Find if possible: sin(nx) a) lim x-4 x2-16 b) lim x (sinx+(cosx)³) (x2+1)(x-3) c) lim,--o (cosx)

A: a) Given that limx→-4sin(πx)x2-16we have to find the limit of…

Q: 1+sin x lim

A: Given that,  limx→∞ 1+sin xx To evaluate  limx→∞ 1+sin xx=limx→∞ 1x+sin xx=limx→∞ 1x+limx→∞sin xx=0…

Q: lim (cos x)x² 1/x2

A:

Q: lim cos x+4e* is 5er

A:

Q: ((주)' lim x (1- cos () COs X->- 00

A:

Q: Find the limits

A:

Q: tan 0 (2) Lim = 1 %3D

A: We first expand the series of tan x and then proceed as explained below:

Q: 4 sin? r d) lim a-0 3x tanx

A: see below the answerHere we use the L'Hospital Rule islimx→af(x)g(x) is of the form 00 then…

Q: i) lim cos x-0 7 πCOS²x x²

A:

Q: cos x lim z-n/2 sin (2x)

A: If limx→afxgx is in 00 form or ∞∞ form; then applying L Hospitals' rule we get:…

Q: tan (5x) x sin3 (2x) 2)- limx-o:

A: we have to evaluate the A=limx→0tan4(5x)xsin3(2x)

Q: 1- cos(x/6) lim II

A: Solve the limit

Q: lim as x approches 0 of cos(6theta)-1/sin(7theta)

A: Given: fθ=limθ→0cos6θ-1sin7θ Apply limit by substituting θ=0 in the above expression.…

Q: et sin x — х - lim x → 0 5 cos x – 5 ||

A:

Q: sin(3 – x) lim с2 — 5х + 6 x→2 x2 – 5x + 6

A:

Q: H.W. Find x-sinx 1. lim X-0 x-tanx

A: “Since you have posted a question with multiple questions , we will solve first for you. To get…

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

A:

Q: tan (x – 2) sin(r – 2)4 Evaluate: lim -

A: we want to find the value of limit   limx→2tan2(x-2)sin(x-2)4

Q: 2 |-cos X lim b. X - Sin x

A:

Q: sinx (4) lim X→T X-TT

A:

Q: (1) lim,o In (sec x) 3x (2) lim, (tan x)*

A:

Q: sin(4x) g) lim

A:

Q: [sec² x (1 + tanx) Vtan² x – 9 tan* x| dx

A: Formulae used:…

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.