tan(In x) 1. Evaluate: dx A. In cos(In x) + C c.tan?(In x) + C B. In sec(ln x) + C D. tan(In x)² + C

Q: Evaluate the indefinite integral. sin(x) cos(9x) dx = +C

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Q: Q2/a) Find the integral f tan5x dx cos³x b) Find the integral cos*x dx 1-sinx

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Q: Q2) 1- Find for: y= cos (x)+cos(x*) CoS

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Q: dx - = In[F(x)]+C•What is F(/3) if C = 0? For (x+x³) (x Tan-lx+1) -1 + - -1

A: Solved below

Q: (a) Find dy/dx for 3 tan x – In x x2 (b) Find f"(x) for the following function: e" In(x**) f(x) = x…

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Q: dx -= In[F(x)]+C. What is F(/3) For (x+x³) (x Tan-lx+ 1) 3. B.

A: We have to choose the correct option according to the given information

Q: 68) Find a value of c that will make sin2 4x 0 x2 f(x) = C, x 0 continuous atx = 0.

A: Given,

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: Find cos (z+2) dx. O-sin (x + 2) +C O sin (x4 + 2) +C O sin (x* + 2) +C sin (2* +2) +C

A: Let's find.

Q: To evaluate 3cos x=1 dr. the integrand can be transformed to 1-sin2x A.) S(3cos³x + csc?x)dx B.) 3…

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Q: For x >0, tanh(Inx)+ dx x2 - (tan-(x)) 1 + > = x? .2 Select one: O True O False

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Q: S cose de 1-sine sece tane de sece - 1 The integral fo fse Si x dx x²+√√√x²−1−1 sino de 1+ cose…

A: we have to above integration

Q: -sin (In x?)ecos² (In x) dx 100x2-x2e2 cos (In x)

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Q: Evaluate the indefinite integral. | = sin(x) cos(4x) dx +C

A: Given query is to find the intersection.

Q: bx + c Given tan 3 - In(x2 - 8x + 25) + 1 -dx %3D x2 - 8x + 25

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Q: d) f(x) – e) f(x) = sin [In (x² - 3x)] sin x f(x) = 1+COS X

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Q: Q3: Let cosh(x)3D5, x>0 , Find values of: sinh(x), tanh(x).coth x ,sech x,csch x

A: Given, cosh(x)=5, x>0

Q: Evaluate the given function tan²ydy = sin3 xdx is equal to.. 3(tany – y) 30 + cosx А. Зх - cos³x…

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Q: For cos2(xy) = L. For cos2(xy) =-, evaluate y' when x = 1. 4 3

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Q: Evaluate: S2-* tanh21- dx 4. A. –In2 In | cos h21- |+C C. In | sec h21-x | +C In 2 B. -4ln | sech?…

A: We are authorised to solve only one question, please repost remaining questions. Indefinite…

Q: Define h(x) = x³ sin(1/x) for x + 0 and h(0) = 0. By using the product and chain rule we know that…

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Q: (B) The evaluation of f- -dx is (x*+3x2 +1)[tan-( In|tan"+5| + e -In tan-( +c (i) (ii) (iii) None of…

A: No antiderivative could be found within the given time limit, or all supported integration methods…

Q: Find the absolute extrema on the interval [0,2π] for f (x)=x/2+cos x.

A: Absolute extrema

Q: Find the absolute extremum point(s) of f(x) = e1−cos x  on [−π/2, π), if any.

A: The given function is                                            f(x)=e1-cos x And we have to find…

Q: 1. Evaluate 1 (a) [ In(2x + 2)dx (b) [ sec'3x tan 3x dx

A: (1)(a) Use the method of substitution to solve the definite integral.…

Q: 33. Prove for a > 0: dx x2 + a 1 tan Ja

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Q: 8) S dx it sinx + cos x a) in (1 + tan =) + c b) In (i - tan £) + c c) - In (1 + tan x) + o 2 d.)…

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Q: 2 tan 4x dx The is equal to 1- tan 24x A. In(sec 8x) + C B. In(sec 8x)8 + C 1 C. In(sec 8x) + C D.…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Evaluate si (z* - tan(z) cos(z) ) dx 2-1

A: To find the integral: ∫11x2-tanxcosxx3-1dx

Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(n/4) = 9?

A: f (x) = cx + ln ( cosx)To Find: For what values of c is f' (π4) = 9Proof: We will differentiate f(x)…

Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: The integral S (A S- (в x dx x² + √√√x²-1- sino do 1 + cos sec²0 do 1+tano " cose de 1-sino sece…

A: Use trigonometric substitution

Q: - (2D³ – D² + 1) (In cos x – 2 tan x)

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Q: 1. Determine the absolute extrema of f(x) = (sin x – 1) cos x on 2' 2 if they exist, and identify…

A: Given:-f(x)=sinx-1cosx,        x∈-π2, π2f'(x)=sinx-1ddxcosx+cosxddxsinx-1…

Q: [sin(In x) + cos(In x)]* dx 3. xp: 3x/10 In(3x) – (In(3x))²

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Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: 1. Determine the absolute extrema of f(z) = (sin a – 1) cos z on -. 2 if they exist, and identify…

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Q: e* (1 + sin x de. nx] Evaluate 1 + cos x

A: I am attaching image so that you understand each and every step.

Q: Find the intervals on which f(x) = 5 x + 5 cos(r) increases for 0 < a < 2n.

A: f(x) is increasing if f'(x)&gt;0 in the interval   Note that  -1 less than equal to (sinx) less than…

Q: Evaluate the indefinite integral. cos x dx (sin x)27

A: Let's find.

Q: Find this second derivative: dz O 2 cos a? – 4x² - sin x² O 4x² cos x² – 2 sin æ² O 82² (cos z²)…

A: Given : Second derivate of sinx2

Q: For sin y=- find the value of so that (y+y")= - 1 at 1 at x=0 Cos X-

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Q: cos x -dx Compute the integral 1+(sin x)²

A: replace sinx=u cosxdx=du limits of u will be 0 to 1

Q: proximation at z = 0 to sin(4r) is A + Bx where A is:

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Q: 2tan x In (cos x) dx= A sin x [In(cos x)] + c cos x [In(cos x)] + C © -[In(cos x)]? +C D [In(sinx)]?…

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Q: xy−cos(xy)=1 implicitly differentiate

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Q: dy - y tan x = 10 tan x dx ution of y(x) using two different techniques. Hint: tan x dx = - In(cos…

A: We have to solve given problem: First method:

Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is  f '(π/4) = 9?

A: Consider the given function, fx=cx+lncosx first differentiate the function using chain rule as…

Q: Using an appropriate substitution, f sin®(x)cos³(x)dx is equal to:

A: