Show that the function f(x)=x^-4 +cos(-2x) is even, odd, or neither."

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

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Q: 3x+4 3. f(x) = x2+3

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Q: Determine the absolute extreme values of the function f(x) = sinx - cosx + 6 on the interval 0 ≤ x ≤…

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Q: Suppose a metal ball is heated in an oven at 195 °C for a very long time. After, it was removed and…

A: Let the temperature of metal ball at time t be:  y(t) Surrounding temperature is:  A = 25°C…

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: Choose the correct answer by using the Product rule of derivative. d dx - (x4.x7) is equal to…

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Q: Find y' by in differentiation 1.) y= (x^2 + 1)^4 (x^3-10)^5 2.) y= 6x^2 (x+5)^3 / (2-x)^2

A: (1)      ddxx2+14x3-105 Apply the product rule: f·g'=f'·g+f·g' f=x2+14, g=x3-105…

Q: If f(x) = cos(x) +3z³, what is f'(æ)? O f'(x) = sin(x) +3z³ O f'(x) = sin(x)+ 9x² O f'(x) =…

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

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Q: The derivative of the function f is defined by f'(x) = (x² + 2) sin (2x − 2). If ƒ (2) = 7, what is…

A: answer is in next step. please give a like!!

Q: The derivative of the function f is defined by ƒ'(x) = (x² + 2) sin (2x − 2) . If ƒ (2) = 7, what is…

A: Given that the derivative of the function f is defined by f'x=x2+2 sin2x-2.   Also f2=7.   Find: The…

Q: By using the definition of hyperbolic functions, show that sinh x = 1 (cosh 2x – 1). -

A: Given,         sinh2x=12cosh2x-1

Q: Suppose a metal ball is heated in an oven at 195 °C for a very long time. After, it was removed and…

A: follow the procedure given below.

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

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Q: 1. f(x)= Vx3 + 2x² + 3 2. f(x) = (6x – 7)(2x + 3)

A: To find the second derivatives of the given functions.

Q: The first derivative of y=cos(tan(x2-7x+1)) is.. 1. O -[sin(tan(x²-7x+1))][sec²(2x-7)] 2. O…

A: Find the derivative of y=costanx2-7x+1

Q: 2- Find the positive root of f(x) = xe"- cos(x) with an error tolerance =0.005% by using the secant…

A: Using a graph, it can be found out whether a function has solutions if the graph cuts the x-axis at…

Q: Construct an example of an non-homogeneous ODE that cannot be solved using method of undetermined…

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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: Consider the function f(x) whose second derivative is f''(x)=5x+3sin(x) If f(0)=2 and f'(0)=3 what…

A: Given : f''x = 5x + 3sinx

Q: sinh(9x) If g(x) : 8 + cosh(9x) find g' (x) 8+ cosh(0)

A: Following formulae are used to solve first question

Q: Verify the formulas by differentiation. ∫ sec2 (5x - 1) dx = 1/5 tan (5x - 1) + C

A: ∫sec25x-1 dx=15tan5x-1+C

Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: Find the root between [-1,0] where \( f(x)=(x+2)^3+2x-5 \) with error \( \epsilon=0.1\) by using…

A: given equation is fx=x+23+2x-5interval -1,0find the root of an equation by using false position…

Q: 3x+4 3. f(x) = x2+3 12 x3+6x2+3x 4. f(x) = 3x

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Q: 1 Differentiate f(æ) = sin-(4x). Use exact values. = (x),f

A: We use the chain rule for differentiation

Q: : Find value of x if :- 2 sinh (2x) - 4 cosh (2x) = - 4

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Q: Consider the function f(x) whose second derivative is f''(x)=4x+3sin(x)   If f(0)=3  and f'(0)=2…

A: detailed solution with explanation is given below

Q: 2Xin 2. O dy/dx if

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Q: rconh(3x+1) - 5t +ldt f(x)= sinh³

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Q: Find the root between [-1,0] where f (x) = (x+2)³ +2x – 5 with error epsilon=0.1 by using False…

A: The false position method is one of the methods used to find the approximate root of a function in a…

Q: sinx(tan(x/2))-sinx=0

A: sin x tanx2-sin x=0

Q: Find the possible values of cosh x that satisfies sinh²x – 3 cosh x + 3 = 0

A: We use the following identity to solve question 1). cosh2x - sinh2x = 1

Q: Choose the correct value of derivative. d dx x+1 X () is equal to (Hint: Look at the note of section…

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Q: The graph of a particular function passes through the point (3,4). Its first derivative is 2yy' + 2x…

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Q: f(x) = ln(125 sin^2(x))

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Q: Find fif f'(0) = 2 sin 0-sec²0

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Q: Evaluate sin (4x) cos -2(4x) dx. | sin (4x) cos -2(4x) dx = O

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Q: If f(x) = sinx + cosx sinx - cosx 2 show that f'(x) = sin 2x – 1

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Q: if X #0 メ=ロ Frnd continuous

A: given the function fx=xx if x≠00   if x=0 we know that x=x if x>0x=-x if x<0 therefore,…

Q: The derivative of the function f is defined by f'(x) = (x² + 2) sin (2x − 2) . If ƒ (2) = 7, what is…

A: Given f'x=x2+2 sin2x-2. Also given f(2) = 7.   To Find: The absolute minimum value of the function f…

Q: f(x) = (6x – 7)(2x + 3) %3D

A: Given  f(x)=(6x-7)(2x+3)

Q: X-2 %3D

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Q: (b) Verify that f(x) = 2 cos(x) sin(x). f(x) = sin(7x) + sin(8x) 7x + 7x = 2 sin 2 = 2 sin |co(-)

A: Let the function is  f(x)=sin(7x)+sin(8x)   Formula used: Sin(a)+sin(b)=2sina+b2cosa-b2

Q: 7. Find the first 2 iterations for the root of f(x) = x- cosx by the Secant method on [0,1.

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Q: 12. f(x) = ( cosx 1+sinx)

A: f(x)= (cosx/ 1+sinx)2

Q: If g(x) : 8 + cosh(9x) find g'(x) 8+ cosh(0)

A: Answer and explanation is given below

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: 26. Show that the function has removable discontinuity at the origin sin 2x {²7, 2x 1 f(x) = if x =…

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