2cos?x – 1 lim tan(2x) sin 5x lim x→0 lim х-о бxsec(3х) x2 + sin 2x lim cos x – sinx 8x 10x

Q: 1 + x + sin x 47. lim 3 cos x 49. lim Vx + 4 cos (x + T)

A:

Q: [xus (2) x+10) xuIsx(p) x(1) (k)1 ×sinx (1x [x][a] (k) 1 x (m)xcosx

A:

Q: 2 cos(4x) – 4x2 – 2 lim - I→0 sin(2x)- x2 - 2x

A: We have to evaluate the limit limx→0 2 cos(4x) - 4x2 - 2sin(2x) - x2 - 2x

Q: 2x sin x is x-0 1-cos x lim A. 5 В. — 5 C. 4 D. - 4

A: NOTE: Refresh your page if you can't see any equations. .

Q: d) lime tan 0 sin 0 3. e) lim0 sin z-cos z+1 3z

A: We have to find the limits .

Q: - i) By using L'Hopital Rule, find sinx lim x-0 e3x 1 ii) Given that a = sin V3 2, find, csca -1

A: In L Hopital's rule take the derivative of numerator and denominator separately and than put the…

Q: 1 - cos(3x) lim 3x х> 0 1 + Зх — е e

A: We , have                Given      lim 1-cos3x1+3x-e3x     x70We have to evaluate the…

Q: -Vx+ 1+ In(x) e* lim + sin (x)cos(x)

A: Find the limit

Q: 0/0 form Evaluate the following limits using l’Hôpital’s Rule.

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: cos x 13. lim x→(T/2)* 1 – sin x

A:

Q: エ→2 x² -4 1- cos 2x 7) lim X sin x エ→0

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 9. If f (x) = sin 3x so lim f(x+2h)+f(x-2h)-2f(x) ... -18h2 А. —3 sin 3x В. —2 sin 3x C. sin 3x D. 2…

A:

Q: 1. fcosax tan(sin ax)dx - In |cos(sin ax)|+ c ans : or In |sec(sin ax)| + c 2. Ssin(cos.x)·sin x dx…

A: Here we use the other formulas with the given one and also use substitution.

Q: П 9. In(1+ kx) sin r x(ekz – x – 1) lim \k=2

A:

Q: find 49. lim 0 - sin 0 cos e tan 0 - 0 sin 3x - 3x + x² 50. lim sin x sin 2r

A:

Q: sin°(,² – 4) (x+2) tan(x+ 2 limy→-2

A: We have to solve

Q: 1. If z=ln (x-y) +tan (x+y) find zxx and zyy

A: Given: z=lnx-y+tanx+y  ……1

Q: 16 |how do you express limn→0 0 Li=1 - (5+ £)9/ as п definite integral

A:

Q: 4x[ cos (2x) – 1] sin (5x) – 5x Use L'Hopital's Rule to evaluate lim 4x[ cos (2x) – 1] lim sin (5x)…

A:

Q: 3. Show that Σ L 1 L-x= 2 2nnx sin L 0<x<L.

A: Let f(x)='12L-x Fourier half range sine series in 0&lt;x&lt;L is bn=2L∫0Lf(x)sinnπxLdx…

Q: Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that          f(x) = x - cosx…

A: As the intermediate value theorem states that if a function is continuous on a closed interval [a,b]…

Q: i) lim(In (3x– 2)– In(5x+4)) Зх +1 lim 1 j) x0* sin x k) lim (csc x- cot x + cos x)

A:

Q: 2 сos(6x) — 6 2? — 2 os(6x) – 6 x² sin(5x) – x2 – 5x - | lim x → 0 - -

A: We have to calculate the given limit: limx→02cos6x-6x2-2sin5x-x2-5x

Q: 4) lim (1 + sin 4x)¹/x x→0+

A: Given limx→x+1+sin(4x)1x

Q: (c) (d) sin 3x lim z0 tan 3r lim (In(sin 2x) - In(tanz)) +0+z

A: Here we have to solve the given limits.

Q: 2. 2. COS X Sinx lim 4x-X

A:

Q: n lim >(sin (2mx;))Ax over [0,1] i=1

A:

Q: x² +9 √(x² - 1)(x^² + 4) In 1x + 11 + In |x-1| + tan-¹) + C Option 1 In x +11+ In |x-1|-tan ¹ () + C…

A:

Q: Vx 6. lim x00 In(x1000) 7. lim 3*-2x X0 x2-x 8. lim 35 sin (nx) cos2 (Tx) 9. lim X-5 2n2(x-5)2

A:

Q: (1) lim (In ) = z (x1 (j) lim rsin z x→0+ sin 2x + 2 arctan 3x + 3x2 (k) lim x→0 In (1+3x + sin? x)…

A:

Q: x cos (3x – 7) cos(2x+ 7) lim cos(플-x)

A: Limits

Q: lim * In(sec(2x)) x→0 (sin(3x))³

A: To find the limit.

Q: 4 points lim h→0 2h cos(x² + 1)dx O 1 O cos(1) O sin(1)

A:

Q: SV1+ sin2(x - 2). sin (x – 2). cos (x – 2) dx

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 4. y = √esinx + 2 5. y = 4x In 4x 6. xe = sin 5x - sin 3y

A:

Q: (7x – 10,* lim x+0 7x lim 2x sin- 9 sin 27x lim x2 21x lim x+00 12 – 3x

A:

Q: The limit lim (18 x; - 28 sin (x;)) Ax i=1 on the interval 0, is equal Tt/4 | (9 x² + 28 cos (x)) dx…

A:

Q: 2 sin (4x) lim 2. x2 (1+ cos x)

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: tanx 4 – lim 0 Cos[1– –] X 0.7 O 1.5 O 0.5

A:

Q: X+ 0.4Inx 04. limx→+o X+ 3lnx 05. lim, „(e* – 1)cosx e' – 1)cos> COSX 'x→0

A:

Q: lim as x approaches 0   x sin(x)/1-cos(x)

A:

Q: 2x + Vx x² + 4x 3 1. lim 2. lim 7x2 + 2 sin x 3. lim x→-o x + e* 4. lim et 2xe2x In x 6. lim 5. lim…

A: To decide whether the given limit produces an indeterminate form6. limx→∞lnxx

Q: 1. Lim 2×ー2xーメ+1 x-x3- 2x + 2 3. Lim メ→。 |- Cos X X-1 Sin 2x 2. Lim csc ax Csc 2x 4. Lim 7X 2x+5 x-…

A:

Q: 1.) lim 2x sin'x. *P0 ex - x - 1

A: We apply l- hospital rules and solve it. Follow 2nd step.

Q: 6. Using a suitable substitution in each case, integrate the following w 1 (a) x2 + 10x + 29 sec?,…

A:

Q: S lim 1 (1+x)2+n³ cos (nº + x³) dr

A: HINT:  Used Integration formulas and limit formulas.

Q: 5. Find the PARTICULAR SOLUTION: y' = 1+ 3y tan x when x = 0 ; y = 1

A:

Q: 1. lim 3r+2r+1 X-n Sx2+7x+4 2. lim +sinx

A: See 2nd step

Q: Find 2 sin(x + sin(x + sin a)) – 2 cos(cos 1) lim 2x – T ithout using L'Hôpital's Rule.

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.