Suppose that f (x) = 0.5 cos x for -"/2

Q: Suppose thnat the tangent line to the graph or J is equal to the tangent line to e graph of g(r) =…

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Q: Compute cosh x and tanh x, assuming that sinh x = 0.8.

A: Here given as sinhx=0.8 Use the identity…

Q: Graph the function defined as follows over a two-period interval. y = 2 cos x

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Q: Graph the function defined as follows over a two-period interval. y = -sin x

A: Graph of the function can be drawn with the help of some arbitrary points. Substitute some…

Q: if f(x)=ln(1+cosx) then find f`(x)

A: f'(x)=(1+cos(x))'/(1+cos(x))      =-sin(x)/(1+cos(x))

Q: (b) Prove that : - 1) (coshx)2 – (sinhx)2 = 1 ,2) coshx- sinhx = e-*, 3) (cothx)? -1= (cschx)?

A: Given that  The following

Q: EX / Show that cosh x-sinhx=1

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Q: Find an upper bound on the error that can result if cos(æ) is approximated by 1– (x/2!) + (x*/4!)…

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Q: 2. Find the root of the function using Fixed-point Iteration. f (x) = x cos (x) - x?

A: Consider the given function as, fx=xcosx-x2

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () < 0, f(x) has a root in [0]. If we use…

A: For finding a zero of a function f, the secant method is defined by the recurrence relation.…

Q: 26. Show that the function has removable discontinuity at the origin sin 2x 2x f(x) = {Z 1 if x = 0…

A: Given f(0)=1 now we have find   limx→0f(x)=limx→0(sin2x2x)=1  ( By property)

Q: -1 We can conclude from the derivative of sin-1(x)and cos-1(x) that sin-(x) + cos¯(x) is constant.…

A: Explanation: find the derivative of sin-1x &amp; cos-1x

Q: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

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Q: 1- Prove that cosh 2x - sinh 2x = e2

A: sol)Given cos h 2x-sin h 2x=e2x

Q: 1. Estimate the root of the expression, f (x) = x² – cos x, using: b. False Position Method in the…

A: If the root of a function f(x) lies in the interval [a, b] and f(x) has opposite signs at a and b,…

Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

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Q: If f(x)=4x(sinx+cosx), f′(x). f′(x) =   Evaluate the derivative at x=5. Enter an approximation,…

A: Given,         fx=4xsinx+cosx

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, ƒ (x) has a root in [o,]. If we…

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Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: 3. Compute 4 (sin? x + cos? x) without using the derivative formulas for sin x and cos x.

A: Given:

Q: (3) Estimate the error involved in using the approximation cos x = 1- for |x| < 0.01

A: To estimate the error involved in using the approximation cosx≈1-x22 for x≤0.01 The Taylor series…

Q: 7. The derivatives of the function f (x) = cos(3x²) that follow are incorrect. What misconception…

A: The differentiation of product two functions can be calculated by using the formula,…

Q: If f(x) Files = Time left 0:5 sin²x and g(x) = 1 + cos²x, how are f'(x) and g'(x) related? Maximum…

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Q: (b) Prove that : - 1) (coshx)² – (sinhx)² = 1

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Q: f'(t) = sin 8t - cos -/-

A: You are correct

Q: 31. Verify the formulas sinh-x = In |x + Vx² + 1| coshx = In |x +Vx² – 1| (for x > 1)

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Q: Use false position method to find the root of f(x) = e* (3.2 sin x - 0.5 cos x) on the interval…

A: We need to find the root of fx=e-x3.2 sin x-0.5 cos x The given interval is 3,4 Also, we are…

Q: Compute coshx and tanhx, assuming that sinhx = 0.8.

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Q: Prove Formula 6 for the derivative of Cos-1 by the samemethod as for Formula 3.

A: let y=cos-1x   then cosy=x Differentiate the equation cosy=x with respect to x.…

Q: Use Simpson's rule with n = 4 to approximate 3 cos(x)

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Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = -2…

A: Differentiate the function f(x)=-2cos x-x with respect to x to obtain the value of f'(x) and equate…

Q: Use Simpson's rule with n = 6 to approximate cos(x) rp-

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Q: Verify the identity cosh 2x = cosh2 x + sinh2 x

A: we have to verify the identity: cosh(2x)=cosh2x+sinh2x   L.H.S: cosh2x as we know that coshx=ex+e-x2…

Q: Which of the following has a derivative of f (x) = 2x (arctanx + arccotx)?

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Q: Use a calculator to compute sinh x and cosh x for x = −3, 0, 5.

A:

Q: 3. Prove that: cosh x - sinh x = e¯*

A: Proved Coshx - Sinhx = e-x

Q: Find sine half range for f(x) = \cos xl for -1<x<1 COSX for 7 < x < 0. f(x) for 0<x< 7. COSX

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Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = 3 cos…

A: fx=3cos3x Differentiating with respect to x, we get f'x=3-sin3x·3=-9sin3x Now,…

Q: 15. -- sin(2+ 2) dz

A: According to the given information, it is required to solve the give integral.

Q: In(cos(x)) Find the derivative of cos(In(x))

A: Derivative using quotient rule (f/g)'=(gf'-fg')/g2

Q: 4. Use implicit differentiation to find az in xexyz sin(2z) – xyz = 5. ду

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Which is the derivative of y= sin In(5x +2)? * 5 cos In(5x + 2) In 5 5Cos In (5x+2) 5x+2 O Option 3…

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Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

Q: Find sine half range for f(x) = \cos x for -t< a <n %3D cosx for f(x) for 0<x <n. cosx

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Q: Find the term representing the fifth harmonic for the periodic function of period 21 given by:…

A: find the term representing the fifth harmonic for the periodic function of period 2π given by…

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () <0, f(x) has a root in [0]. If we use…

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Q: Differentiate the following functions 4 1-cos2x Y = by chain rule. 1+cos2x

A: To differentiate the given function.

Q: Find the exact value of the function: 0 6 arccos (-/-)

A: See this solution in below

Q: 3. Write equation of the tangent line to the graph of the function f(x) = ecosx at one of the values…

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