o lim x-0 x² - sin²2x 2 x 2

Q: limg-0 2x sinx 4-4cosx

A: We can find the limit as below, using L'Hospital rule.

Q: lim,-2 3x? – x – 7 |

A: Applying limit property

Q: JO π 3 sec³ x tan x V √2 + secx dx

A:

Q: S(1 + sinx)-1sinxdx

A:

Q: d Find tan1 x + csc¯1 | dx

A: To find ddxtan-1x+csc-1x We know that ddxtan-1x=11+x2 ddxcsc-1x=-1xx2-1

Q: 3 Lim x40 Cosx (2 Cos²x - 1) Cosx -

A:

Q: I 1 -x² + 4x - 5 A B D dx _____ In-x² + 4x −5+ C -tan-¹(x - 2) + C -tan-¹(x + 2) + C tan ¹(x - 2) +…

A:

Q: sin 5x lim, X→0

A: Given, limx→ 0sin5xx   Apply the L'Hopital's Rule: limx→ 0sin5xx=limx→ 0cos5x· 51

Q: 9. Simplify sec² x - 1 sec² x

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

Q: COS X lim x0x +3

A:

Q: secx-secx COS x 2+anx sinx-secx

A: Given To simplify sec x -sec x.cos2 x2 tan x - sin x.sec x

Q: sin (an) - 3cos² (5n) √5 n

A:

Q: find x 3tan(x-15)=tan(x+15)

A: Given

Q: lim x2 + 4х + 3 X→-1 1 O 2

A:

Q: 1 sint j+e3t t valuate lim t0 2t +5

A: Given: The limit is limt→0 12t+5 i + sin tt j + e3t k .

Q: y" + 16y2x sin 4x

A:

Q: lim, 0 6 tan² (5x) 15x²

A:

Q: 2 X-9 Sinx +34 2

A: Hi ! Thanks for posting your question. Since our portal allows to answer only first three questions,…

Q: +lim x-0 e -x - 8x ex - e x - sin x

A:

Q: . lim e²x-1 X30 3x+4 sinx

A: given limit is of 00 indeterminate formso, apply the L'Hospital's rule to solve the limit

Q: Find y lnxy tan (X+9)

A:

Q: 1. S x(x2022+1) dx

A: The given problem is solved below in detail.