write a formula for f ogo h X +2 f(x) 3-x g(x) || 2 X' x +1 h(x) = v2- x /2-x X

Q: The maximum value of F in F(x) = - 4 cos x is 2 4 1

A: We know range of cosine function is [-1,1] Therefore maximum value of f(x)= -4cosx is, f(x)=-4cosx…

Q: 4. Determine the root of F(x) = 7 sin(x)e-x – 1 using secant method with 3 iterations glven Xi-1 =…

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Q: 2. If f(x) = cos2x, find f(0), f(--).f),f(-x) 3. If f(x) = x(x+1), show that f(x+h)– f(x)= h(2x +1+…

A: 2. f(x) = cos2x , find f(0) , f(-π/4), f(7π/8) ,                                         f(-x). f(0)…

Q: ln(x) is just defined for x greater than 1. Select one: True False

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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: Find a root of an equation f(x)=x3-x-1 using Newton Raphson method.

A: We will find out the required root.

Q: Find f'(x). f(x) = O O O 6x - sin² (5x) f'(x) = O f'(x) = f'(x) = f'(x) = = 6-10sin(5x)cos(5x) 2√6x…

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Q: solve using reduction of order (D^2+1)y=tanx

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Q: 1.Find the interval and radius of conv. of ln(1 – x²) ?

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Q: Find f(x) if f "(x) = x -cos x, f ' (0) = 2 and f(0) = -2.

A: To find f'(x) from f"(x), we will integrate f"(x) c=integrating constant Given f'(0)=2 , using that…

Q: 2) Use Newton's method to approximate the zero in f(x) = - x3 + 3x-x + 1, or explain why Newton's…

A: Consider the given function,

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: Apply the Mean Value Theorem for the function f(x) = 2 ln(4x + 7) over the interval [1,3]. Show your…

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Q: Let f(x): e² sin³ (4) x6 sec(x − 2) a. Solve for f'(x) without using quotient rule or product rule.…

A: As per the question we are given the function f(x) and we have to find its derivative f'(x)  without…

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: Use Taylor's polynomial of degree 2 of the function f(x) = tan 1(x+1) + x² %3D about c = - 1 to…

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Q: Suppose f''(x) = -(sin(x)), f'(0)=6 and f(0)= -1 Find f(π/2) =?

A: Given query is to find the value of the function at indicated point.

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

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Q: Find the smallest positive zero of f(x)=cos^2(x)-sin^2(x)

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Q: 3. Evaluate f x sin2 (x²) dx.

A: Given I=∫x sin2x2 dx To Find I

Q: Differentiate the function:  k(x) = 4 ln (x) + 2 cos x + x^2 k'(x) =

A: k(x)=4ln(x)+2cosx+x2Differentiate with respect to xk'(x)=(4×1x)+2-sinx+2xk'(x)=4x-2sinx+2x

Q: Use Newton's Method with the function f(x) = x² – 2 and initial value xo = 1 to calculatex1,X2, X3 .…

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Q: Use the mean-value Theorem to prove 1 1 - < ln(x + 1) − ln x < - X x +1

A: Consider the function f(x)=ln(x) So, f(x) is continuous on 0,∞ and f(x) is differentiable on 0,∞.…

Q: Expand tan(x) in powers of x up to first six terms and estimate the value of the function with x…

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Q: Find the value of xg in 3 decimal places (positive root) using Secant Method (8th Iteration) f(x) =…

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Q: Prove the identity arcsinhx=ln(x+√1+x2).

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Q: 1 1- (-1)". f (x) = 2 sin nx. - n=1

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Q: Use Newton's Method to approximate the zero of the function f(x) = x + x - 1. Start with x1 = 0.5…

A: The given function is f(x)=x5+x-1, with x1=0.5

Q: Use the intermediate value theorem to show that there is a solution to x− √ x−ln x = 0 on the…

A: Use the intermediate value theorem to show that there is a solution to x− √ x−ln x = 0 on the…

Q: Let f (x) = sin(4.x). Find the twenty-second derivative of f (x). D22 (f (x)) = O 42² cos(4æ) - 422…

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

A: Proved Coshx - Sinhx = e-x

Q: Find the value of x5 in 3 decimal places (positive value) using Newton-Raphson Method (5th…

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Q: 9) Find f(x) if f'(x) = 7 sin x + 2x - 3 and f(0) = -3

A: Obtain f(x) by integrating the given first derivative as follows.

Q: what is the value of x in second iteration of the function f(x) = sinx - X +5, in the interval of…

A: According to the fundamental theorem of algebra, every algebraic equation has a root. If the…

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

A:

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 Where is the function increasing and decreasing in…

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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: f (x) = 4 sin(3x + 7) is continuous at every point x = x0; that is, lim 4 sin(3x + 1) = 4 sin(3xo +…

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Q: How do I solve the limit as x goes to -1 for the expression (sin(3x-3))/(1-x) without using…

A: The given limit is,

Q: If x >0, Prove that X - ln (1+x ) > x^2/2+2x

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Q: Estimate the value of df/dx for f(x) = root 8x at x = 3, using any method

A: To find the derivative of f(X), differentiate with respect to X on each side.

Q: Find the value of x5 in 1 decimal places (positive value) using Newton-Raphson Method (5th…

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Q: Find all critical numbers of f(x)=3x+sin(3x)

A: Given,   f(x)=3x+sin(3x) We have to find all the critical numbers.

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

A: Answer and explanation is given below

Q: sech2(In x)

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Q: Find (f-1)(a). f(x) = 5 + x + tan(rx/2), -1 < x < 1, a = 5 (f-1)'(a) =

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Q: Solve for x using secant method using four iterations. Assume xo=1 and x1=1.5 f(x) — 3х* — х + 1…

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Q: Expand the function f(x) = x, 0 < x < 2, in half range sine series. 4 O (A) (#) = - sin()- sin() -…

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Q: =sec (Xty)

A: dydx=secx+y  Let v=x+y  1+dydx=dvdx  dydx=dvdx-1  dvdx-1=secv dvdx=secv+1 dvsecv+1=dx

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.