Compare the accuracies of the approximations sin x = x 6x/(6 + x²) by comparing the graphs of and sin x = f(x) = sin x – x and g(x) = sin x – (6x/(6 + x²)). Describe what you find.

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: Integrate sin^2(7x)-cos(x)

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Q: Find a rational (fraction) approximation for the value of 3√11 (square root 11, it wouldn't go…

A: We know that linear approximation (by using the tangent line to f(x) ) of f(x) at point (a,f(a)) is…

Q: A) By using simple Iterative method, find one root of the equation sin x = Use 3D. %3D (x2- In x)3

A: We have sinx=1x2-lnx3 Now, if we need to find a solution of fx=0 then we write fx=0 in the form x=gx…

Q: find f'(x) if f(x) = tanh(ln x) +sin2(2x)

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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: 응(2cosh(sinfx-v)- 8. x² cosh(sin(x 9. 10. V+coshz

A: Partial derivative of f(x , y) w.r.t. x can be found by differentiating w.r.t. x keeping y constant…

Q: Consider the function f(x) whose second derivative is f”(x) = 10x + 8sin(x) If f(0) = 2 and f’(0) =…

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Q: Find f' (x) for 8 sin(x) f(x) = -; 7x2 – 8 sin(x) s'(x) = |

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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 slope of the graph of the function at the given point.

A: We have the given function as fx=4x5+3x-sinx          ⋯⋯1 As we know that, slope of a function fx is…

Q: 6. Differentiate. a) f(x) = In (sin²x) b) g(x) = In (xe-2*)

A: Write sin2x as (sinx)2 and simplify the terms and use the log property to simplify the term and…

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

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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: .Find a reduction formula for ea* sin" x dx. Hence evaluate e* sin x dx. 3

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Q: Sin x3D%=

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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: Find the slope of the graph of the function at the given point. f(x) = 4x5 + 2x - sin(x), (0, 0)…

A: We havefx=4x5+2x−sinx

Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: Find the second derivative of f(x) = 9 sin (2x). Enclose arguments of functions in parentheses. For…

A: On solving this we will get

Q: find the root of 3x +sinx -e ^x=0 using secant method

A: Let us consider the function fx=3x+sinx-ex. We have to use the secant method to find the…

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

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Q: 3. Evaluate f x sin2 (x²) dx.

A: Given I=∫x sin2x2 dx To Find I

Q: Find first and 2nd derivative guncic 2 tan2x 3.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Show that sin(x^2) ≤ sin x for 0 ≤ x ≤ 1. Deduce that sin(x^2) dx ≤√2/2 on the invterval [0, π/4]

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Q: Find the root of the equation using any bracketing method: f(x) = x2 – sin x - 0.5 with an upper…

A: Bisection Method:This is one of the simplest and reliable iterative methods for the solution of…

Q: Find the slope of the graph of the function at the given point.                         f(x) = 4x5 +…

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Q: Estimate the error if P3(x) =x- is used to estimate the value of sin x at x= 0.4.

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

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Q: Solve x - cos(x) = 0 by Secant method. Use x-1 = 0.5 and xo = 1.0 as the initial estimates. %3D

A: We will find roots till 4 digit repeat

Q: Explain graphically why there is no solution to cosh x = sinh x

A: cosh x = sinh x. We need to explain graphically why there is no solution to the given equation.

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: 2. Use the identity of inverse hyperbolic function to solve cosh-(2 – a2) = ln 2, for |æ| < 1.

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Q: Find the linear approximation of f(x)=sin(x) at x=3π4 and use it to approximate sin(134∘). Give…

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Q: find g' g(x)= square root of 1-sin^2(x)

A: The given expression is: g(x)= square root of 1-sin^2(x)I am interpreting it to be as shown on the…

Q: The approximation of the root x* of the function f(x) = -x + sinx-1 accurate to within 10-3 using…

A: Needs 2 iterations

Q: Use integration by parts to verify the reduction formula.

A: We have to verify the reduction formula using integration by parts: ∫sinn x dx=-sinn-1 x cos…

Q: what is the maximum value of y=sinx, 0 less than or equal to x less than or equal to 2pie, and…

A: Given function  y = sinx on  0≤x≤2π

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

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Q: Compute for a real root of sin√(x) -x = 0 using the fixed point method with x0=0.50 until absolute…

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Q: Find the root using newton raphson method for f(x) = sin(x) − x²

A: Given function is f(x)=sin(x)-x2 From the given equation, it is clear that 0 is one of the root of…

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 derivative  f(x) = cos-1(3x) sin-1(3x)

A: To differentiate the function with respect to x.

Q: Find the derivative. Simplify completely. 1. f(x) = 4x³ cos x 2. g(x): Sx-4 In x 3. у sin x 4. f(x)…

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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: 2. 1 Given: cosh x==(e* + e*), =(e* - e**), use these sinh x = definitions to show that cosh²x-sinh2…

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

A: Answer and explanation is given below

Q: Find the linear approximation to sin(x) at the point x-0 and use your answer to approximate the…

A: Given f(x)= sin(x), a=0 we know linear approximation, L(x)= f(a)+f'(a)(x-a)