2 lim (x + 6) sin(3x) cot (x² + 6x) X→0

Q: lim (x' - 2x² +5)=. – 2x² +5)= x→-2

A: Please refer to the image below. 9

Q: Show that ⊢ (x > 0) y = x + 1 (y > 1)

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Q: (sinx -) tan*(5x) Q3/ 1)- lim, 2)- limx-0 (3sin?x -sinx +1) x sin3 (2x)

A: There are multiple question. As per Bartleby policy Kindly ask other question separately.  Given…

Q: 8 him XT 2 (secx tanx) 1

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Q: IfY C X, show that inf (X) < inf (Y)

A:

Q: Find the derivative of y sin ¹(3x) x sin ¹(3x)-3x√1-9x²-9x² sin ¹(3x) x² (1-9x²) sin…

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Q: x+2 lim sin - x+6x+8 3 2.

A:

Q: 3x2-7x+8 f(x) = Find f'(x) %3D sin (5x2+9x-6)

A: Here we use division rule of differenciation.

Q: 9. Simplify sec² x - 1 sec² x

A: secx=1cosxI=sec2x-1sec2xsin2x+cos2x=1

Q: Vx+1- /2x x² - x 2х f ) lim x→1

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: lim

A:

Q: 6. f tan x secx+4 cos x - dx

A:

Q: 4x+sin x lim x→02x - sin 3x

A: We have to solve given problem:

Q: dx J x²–18x+97 O fIn (x² – 18x + 97) + C In (x² – 18x + 97) + C 0sin-l (부) + C х-9 O tan-' () + C…

A:

Q: X-yi/x2+y2=1/(1+xi)(3+i)

A: Given

Q: sin5x(1-2t)dt (6) lim

A: limx→0∫xsin5x1-2tdtx Let  I=∫xsin5x1-2tdt=t-t2xsin5x=sin5x-sin25x-x+x2

Q: 2. Prove that d [(2x+1)³] (2x+1)³(4x-19) (x-3)² dx = Then, -5 (2x+1)(8x-38) 3(x-3)² dx.

A:

Q: 2x² + cos(3x) *-* x²-10x+cos.x b) lim

A: Given Expression for the limit is as follows

Q: L {5-e²t +6t2} L {t²-3t 2e sin(3t)} MA L {t-t²-t+sin(√2t)} D

A: Laplace transformation formulas used are

Q: Sin13*

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Q: sin4x 15. lim x→0 sin7x

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Q: sin(3x)cos(3x) sin(2x) 의[cos(2x)-1]+ +C 12 8 4

A: