(c) lim →0 (d) lim 2 \sın´x 1 - cos(x2) x-x² +0 x² sin x 1 1 (e) lim sın¯x sin(x2)

Q: 1 Evaluate: lim sin2(x) 4 TC 6 6.

A:

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: lim (2,1)→(0,0) xª + 4y²

A: The given limit is,

Q: Find the value of the limit lim SINX X 0 2x 02x (a) 0 (b) 1 (c) 1/3 (d) 1/2 (e) 1/4

A: Here we have to find the limit of the function. In the first step use the property of the limit:

Q: If f(x+y)=f(x)+f(y) for all x , y e R and E(tanx) _ 2f (sinx) f (1) =1,then evaluate lim x’f(sinx)…

A:

Q: 1/a | sin(t")dt Find lim T.

A: We have to calculate the value of : limx→∞∫01xsint2dt·x

Q: (12 sin )( In x) (x3+5)(x-1) Evaluate limx→1

A: Here we have to evaluate the given limit .

Q: X – sinx (i) lim x2 d (ii) ( e2x · cos x) dx (iii) J tan 2x dx d (iv) dx ( sech 2x) 1 (v) -) dx S(…

A:

Q: f" (h+x)-f" tx) Then lim %3D

A:

Q: Find Integral (cos(x) cos (2x) cos (5x) dx : considering cos (mx) cos (nx)= = (cos((m-n)x)+ cos…

A:

Q: 9. Evaluate (a) limx→1 2023_ (b) limx→0 x-1 x-sin x ¹x0 4x5-2x³ (c) lim₂-0 3-1-1-2 2x4-3x³

A:

Q: If lim f(x) = = co then f (x) XCOS cos² X00

A: Given- If limx→∞fx=∞ then fx=xcos1x To Prove- The above expression.

Q: 3e2* -1 d) lim 2x 4e* +cos x

A:

Q: If lim f(x) = L and lim g(x) M, use L, M, or both to complete the statements

A: Given: limx→afx=L and limx→agx=M. To find limx→afx·gx using L,M or both. Solution: Product rule of…

Q: sin(x²) x→0 In(cosx) 4. Evaluate lim

A:

Q: x²-7x+10 1. limx-2 x-2

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

Q: (x)- f(1) lim f(x) = 2 , where x-1 х-1

A:

Q: lim t →0  (e^6t i + (sin(7t)/ (7t)) j + e^−4t k)

A: Limit :

Q: Q4 1-F(x)=limx→0 vV(x2+3)-3}/x2 2- limy 3y+5y2-7 10y3-11y+12 sin4x 3 - lim 0 sin2x

A:

Q: 3x4-x2 2) x"m. (2 + inx) lim lim 1) x4-1

A:

Q: #1. lim t-tvt 213/2 12 +3t – 5 t→ 00 #2. lim x → - o0 x' +1 #3. lim tan1 (In x) x → 0+

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: f" (h+x)-j" (x) li h→0

A:

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

A:

Q: Is there a function f such that limx→1 f(x) = 0 and limx→1 f(x) (x-1)³ = -∞?

A: To find:- A function f such that limx→1fx=0 and limx→1 fxx-13=-∞

Q: TX = tan 4 f(x) = TX tan 4 lim x→-2- TX lim tan 4 x→-2 -6 2 6 II

A:

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: 10. lim ) 1 -1) A-0 hV1+h sin x 13. lim 0 2x-xr V8+x -2 (Hі 16. lim

A: We have to use proper techniques here.

Q: 2²+ cos(x) x 0

A: