Evaluate Stan" (x) sec¹x dx. 1 -tan (+2)(x) +-tan" (x) + C m+2 m 1 1 -tan (+1)(x) + -tan (™-1)(x) + C m+1 777 1 1 tan (+1)(x)tan (-1) (x) + C m+1 1 -tan (+3)(x) + -tan (+1)(x) + C m+1 то m+3

Q: True or false: For any constant C, d [tan(x) + C] = [sec(z)]²

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Q: dx -= In[F(x)]+C. What is F(/3) if C = 0? For (x+x³) (x Tan-lx+1) A + - B 6. + 3 D + 6 + -15 -15 -15

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Q: If f(x) = tan (3x), then f'(x) = (A) 12 tan (3x) sec?(3x) (B) 4 tan (3æ) sec2(3x) (C) 12 tan (3x)…

A: derivative

Q: Let Find f(x)\x= = ". y = f(x) = 31 sec x + 18 tan x 31 sec x 18 tan x d dx -f(x)\ x= 1 *

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Q: Differentiate g(x) = (In(x² + 1) – tan-ª(6x))10

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Q: S(sec a tan x 5æ4)dx tan x + x +c - sec x + x' + c sec x – x5 + c sec x + x +c sec x – x + c

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Q: Q1) Show that: (b) (cosx) = -sinx =1+* (a) (1+x) =1+6x %3! (e) (VF) = (d) v1+ tan x

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Q2/ Find f (x) : 1- f(x) = 4 cos x + 2 sin x 2- f(x) = cos x - x csc x 3- f(x) %3D %3D cot x 1+cscx…

A: As per guidelines we can solve only one question at a time. So the first question can be solved as…

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: 1. 1+tan (0²) = sec (0²)

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Q: 1. Prove that the derivative of tan(x) is sec²(x) directly from the definition of the derivative.…

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Q: tan (5x) x sin3 (2x) 2)- limx-o:

A: we have to evaluate the A=limx→0tan4(5x)xsin3(2x)

Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: e* tan (e*) dx sec2 (e*) – 7

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Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: Find f" (x) if f (x) = tan(x² − 1). ○ 2 sec² (x² - 1) ○ 2 sec² (x² − 1) (1 + 4x² tan(x² − 1)) ○ 2…

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Q: 17. Applying the quotient rule, what is the correct FIRST STEP in finding the derivative of the…

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Q: Find the derivatives – do not simplify a. y= x4- 3square root of x + 5x2/3 +8/x-3

A: ddxxn=n xn-1

Q: 27: let f(x) = tan(x)+ sec(x) find f"(x)

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

Q: 3 evaluate f sec³ (x) tan³(x)dx Select one: sec (x) sec (x) + C 3 sec (x) sec (x) + C 3 sec (x) sec…

A: Let's find integration of given function.

Q: What is the derivative of −9 sin² (-3x³)? O-162x³ sin (-3x³) cos (-3x³) no correct answer O 162x²…

A: just differentiate the given function by using chain rule of derivative and easily find the required…

Q: 1. ſ X (2x-5)² (3-4x) dx.

A: Solution: ∫x(2x-5)2(3-4x)dx Take the partial fraction ∫398(2x-5)-514(2x-5)2-349(4x-3)dx

Q: 6. (a) Express cos (2 tan- ) (b) Express sin (2 cosx) as an algebraic expression in x. (c) Express…

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Q: 419 *Ocosec™* 6d8 is equal to

A: Given integral is ∫sec4/9θ cosec14/9θ dθ

Q: S sec° (x) dx Select one: sec“(x) cot(x) O see't) col62) + ¿( sec(x) tan(x) + ¿In|tan(x) + sec(x)|)…

A: We will use bi parts to solve these type of integral.

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

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