Use trigonometric substitution to evaluate the integral (a) arcsin(r)+C 9x 9 - x² √9-x² (b) 9x + C (c) + C (d) In (x√9-x)+CX dx x²√√9-x² (e) In (x² √9-x²) + C

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

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

Q: Make a trigonometric substitution to evaluate / x V25 – x² dx

A: Formulae used: 1-sin2x=cosx ddxsinx=cosx ddxsin2x=2sinxcosx

Q: What is the coefficient of the x term in Maclaurin polynomial for sin(2x)

A:

Q: Express in exact form: In(x² + 1)dx

A: The definite integral is given as .The aim is to express this form in exact form.Concept used :Apply…

Q: (d) tan¹(x)dr

A:

Q: (d) lim 140 sin(2x) – sin(3x)

A:

Q: Let f(2) = : Part (a) Find the integral of the function f(2)on the circle of radius 8 centered…

A:

Q: Find 8 D. [23²-TVE + ] 2x5 x10 Type your answer without fractional or negative exponents. Use…

A:

Q: Prove: sin (2 cosx) = 2x1-x

A:

Q: tan(2 – j5) j(2-j5) +7- jv2 In(-5)| (3220° – sin 20 + jln5)*|

A:

Q: Find the value of (a, b) so that sin 12x lim x+0 x³ cos 12x Write your answer in the form of (a, b)…

A:

Q: sin x+3 cosr dx. Determine the following rational function 1+cosx

A: We have to first do partial fraction of the given expression.

Q: 9. Simplify sec² x - 1 sec² x

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

Q: What is the domain for f(x)=square root 1-sin x? And explain why x cannot be equal pi/2 and 5 pi/2?

A: We draw graph of function f(x)=square root 1-sin x

Q: Determine the 2.x2 – 4x + 6 dx using the definition. (hint: lim Rn)

A: Given: ∫12 2x2-4x+6 dx  To find: Value of the limit.

Q: Fra) = Sin (2t) Find the 7h taylor Polynomial of

A: Given function is  Fx=∫1xsin2tdt

Q: S dz zlnz (Inz)²-1 Select one: O A. Q B. O C. Q D. arcsec(Inx) + C arcsin(lnx) + C arccot(Inx) + C…

A:

Q: 1) Evaluate / Vx-1 dx

A:

Q: Apply Aitken's A²-method to find a root of the equation sin²x = x² - 1

A:

Q: 1 dx 3 (4-x²) ³/2

A:

Q: * Evaluate. [6x² arcsin(x)]dx

A:

Q: ACBinf fCx) şinf R Cx). X6 A XE13

A:

Q: Suppose frx)=1 Zx+3 Find Of frx). What's it's and the inverse functions Domain Benge?

A: Solve

Q: V 6² — (x − a)². b) Use a trigonometric substitution to evaluate the indefinite integral. s dx You…

A: