11) Consider F(x) = S*sec t tan t dt a) Integrate to find F as a function of x b) Demonstrate the Second Fundamental Theorem of Calculus by differentiating the results in part (a)

Q: In explicit method of hyperbolic PDES, the second initial condition, the one involving g, gives…

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Q: 75. F(x) : (t + 2) dt

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Q: Where is the function f(x) is continuous, such that f (x) : In(1-2x)+sin (x 4x+3 %3D [-1, ] – (-) O…

A: We know, ln(x) is defined for x>0. sin-1(x) is defined for x∈-1, 1. f(x)g(x) is defined if…

Q: Find the maximum and minimum valucs of f(x) = sin x + cos x on (0, 2n].

A: Given function:                      f(x) = sin x + cos x,   x∈[0, 2π] Use the second derivative…

Q: Calculate the derivative In (t)dt da using Part 2 of the Fundamental Theorem of Calculus. Enclose…

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Q: Use Part 1 of the Fundamental Theorem of Calculus tofind the derivative of the function.

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Q: The derivative of:          x^8 f(x) = S sqrt(t)sin(t^8)dt          sqrtx using the fundamental…

A: We will use the formula: ddx∫abf(t)dt=f(b)dbdx-f(a)dadx Note, here a and b both are functions of x.…

Q: Find the derivative of OA. In (tan x) y'= X OB. y' = (tan x) OC. y' = [(secx) ²] x OD. Inx y' = (tan…

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Q: (a) Evaluate the indefinite integral (anti-derivative) d.x Vr2 +1 by using the substitution u = x?…

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Q: Evaluate the integral.  integral  sec 2 x  tan  3 x  dx

A: Consider the following integral:

Q: Calculate the derivative 5¢6 23 dt dz using Part 2 of the Fundamental Theorem of Calculus. 5,6 23 dt…

A: step 1: recalling fundamental theorem of calculus Step 2: interpreting with the given question step…

Q: + Bsin z Differentiate @ wi th xespect to x - - S"d (use dy A sinz + B cose

A: Given that: y=Acosx+Bsinx

Q: 3. Show that the complex function f(z)= cscz =1/ sinz satisfies the Cauchy-Riemann condition. Find…

A: The given function is fz=cscz=1sinz. A function fz=ux,y+ivx,y, satisfies Cauchy Riemann equations…

Q: Let f(x, y,z) = z-sin(xy), x = t, y = ln t , z = et-1 . Find derivative of f directly and by using…

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Q: Integrate to find F as a function of x, and demonstrate the Second Fundamental Theorem of Calculus…

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Q: Find F'(x), where F(x)= int. of ((t^2)+1)dt, from sin(3x) to x=-4. Use the 1st rule of the…

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Q: Use integration by parts to prove the reductionformula.

A: Consider the following integration by parts formula: ∫uvdx=u∫vdx-∫dudx∫vdxdx ILATE Rule: We have two…

Q: Explain how the Fundamental Theorem of Line Integrals and Green's Theorem are both similar to the…

A: Statement of fundamental theorem of calculus:

Q: tan °(ln z) sec® (In z) Evaluate dz.

A: Evaluate: ∫tan3lnxsec6lnxxdx

Q: 5. Verify whether the function f(z) Cauchy-Riemann equations or not. sinh 4x cos 4y + i cosh 4x sin…

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Q: Find the integral of * dx 2 sin x – cos x - |tan + 2 + v5 + C tan + 2- V5 In | tan + 2+ v5 |tan + 2…

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Q: Determine whether f(x) is differentiable at x = 0. Show your work. sin(x) cos(x)-1 3x + 1 f(x): = if…

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Q: Sketch the graph of two functions g(x) = cos x and h(x) = on the same plane. Choose [a, b] that…

A: Given g(x)=cosx and h(x)=x/2

Q: Verify the integration formulas in Exercises 37–40. sech x dx = tan'(sinh x) + C 37. a. sech x dx =…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Let u = x3 + 1. Indicate how the limits of integration should be adjusted in order to perform the…

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Q: Use Part 1 of the Fundamental Theorem of Calculus tofind the derivative of the function.

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Q: Sketch the graph of two functions g(x) = cos x and h(x) : plane. Choose [a, b] that satisfied |b –…

A: Given function is g(x)=cosx and h(x)=x/2

Q: :Show that the function 1 x sin When x + 0 S(x) =- 0, is continuous but not differentiable at x = 0.…

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Q: (a) The centripetal acceleration of a particular wheel in a locomotive with respect to the angle…

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Q: Exercise 4. find the indefinite integral and check your result by differenti- ation t2 +2

A: If you like the solution then please give it a thumbs up...   The Answer is:    I = t - 2/t  + c ,…

Q: Show that the integral is independent of the path, and use th Fundamental Theorem of Line Integrals…

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Q: Integral of cos2x on [0, infinity]

A: We have to use limits to find the given integral.

Q: (10) Find the indefinite integral .csc². -dt cot x sec x tan x sec x -1 1 (S- dx (1+ x' 1/3 + 2e* +1…

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Q: Find the integral of * dx J 2 sin x – cos x tan + 2 + V5 + C tan+ 2- V5 V5 |tan + 2-V5 V5 In tan+ 2+…

A: Option 2 will be correct choice.

Q: If we discuss the derivative of the function f(z) = z. Imz by Cauchy- Riemann equations. we see fz)…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Use the Fundamental Theorem of Calculus Part II to compute 0. 4 sec (x) dr.

A: Proceed as shown below

Q: 5) Use the Fundamental Theorem of Calculus to define of the function fol=sin (x?+!) ant-derivative…

A: According to the fundamental theorem of calculus, the following expression is to be true if F is the…

Q: Use Linear Approximation to estimate Af = f(3.02) – f(3) for f(x) = sin(). (Use decimal notation.…

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Q: Calculate the derivative d In (t)dt dx using Part 2 of the Fundamental Theorem of Calculus. Enclose…

A: Given that ,ddx ∫x3e5x   ln (t) dtTo apply fundamental theosem,ddx∫a(x)b(x) f(t) dt = f(b(x)). b1(x)…

Q: Explain how to use the differentiation part of the Fundamental Theorem of Calculus 2+sin(41) 3-9 to…

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Q: What are the new limits of integration if apply the substitutior u = 6x + t to the integral sin (6x…

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Q: In (tan (x)) dx. 3. Evaluate J sin(x) cos(x)

A: NOTE: Refresh your page if you can't see any equations. . ..............(1) substitute  take…

Q: Suppose that a particluar funciton f satisfies f" (x) = - (4 sin(x) + cos(x)), f(0) = 3, f'(0) = 5.…

A: f"(x) = -(4sinx +cosx) ,  f(0) = 3 , f'(0) =5 now integrate the f"(x) f'(x) =4cosx -4sinx +c now…

Q: Determine the maximum/minimum point(s) for y=sin 2x– cos x – 4x on the interval 0 <x< 2n . The…

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Q: Find the definite integral using the Fundamental Theorem. 1 dt NOTE: Enter the exact answer. dt %3D

A: To find the definite integral.

Q: Calculate the derivative 33 4:6 dx using Part 2 of the Fundamental Theorem of Calculus. 33 dt = da

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Q: Use fundamental theorem of calculus .4 –dx x In x 2,

A: Follow the steps.