(a) Show that for x ≥ 1, 1 √1+x² 1 > 0. (b) Use part (a) to show that the integral S 1 √1+x² diverges.

Q: let f(x)= X be 1 213 (-√5 < X<√) Y.V Pind P{/X/7/1.5},

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Q: Prove that c = 4 is the largest root of f (x) = x4 − 8x2 − 128.

A: Given function is, fx=x4-8x2-128. To find the largest root substitute x4-8x2-128=0 Let x2=u. Then,…

Q: If x >= 0 and y >= 0, prove that √xy <= (x+y)/2.

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Q: 02: Let f(x)= x' – 7x+ 2, 0sxs1. 1. Show that f(x) has exactly one real root in the indicated…

A: Answer

Q: Find the domains of h(x)=1/(x3+1)1/3.

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Q: I of the equat: nethod will b

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Q: 77. Show that if f is a quadratic polynomial, then the SDQ at x = a (for any h + 0) is equal to…

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Q: 9. Use the Intermediate value theorem to show that f(x) = 2x( – 3 has a zero in the interval [1,2].

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Q: Calculate the first three approximations x1, x2, x3 to a root of f (x) = x2 − 5 using the initial…

A: fx=x2-5,   x0=2 Differentiating with respect to x, we get f'x=2x Now,…

Q: Estimate the error in √(x-1)=1+x/2 when |x| &lt; 0.01.

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Q: Use bisection to find the root of function f(x) = x* – 18 that lies in the interval (1.8, 2.2)…

A: Given:           f(x) = x4-18 The root of f(x) lies in the interval (1.8, 2.2) The relative…

Q: Find the integral of f(x) = 1 √1-16x² between 0 and 1.

A: The given integral is 1/sqrt(1-16x2).

Q: Find the derivative of y = 23 + : dy dz

A: Given that: y=z3+16z

Q: 3) Consider the definite integral [f(x) = √1+². calculate the following: a) Left hand sum using 2…

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Q: Find the best quadratic approximation to f on the interval [ 0, 1].                       f(x) = ex

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Q: Use the Newton-Raphson iterative method to find the root of the function f(x) = x³ + x² + 4x + 3 in…

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Q: Use linear approximation to estimate √(4.01) + (4.01)2 correct to four decimal places.

A: Linear approximation of fx about x=a is given by L(x)=f(a)+(x-a)f'(a).

Q: Given that f(x) = 7x + 5 and g(x) = 8 – x², calculate (a) (f o g)(0) = f(g(0))= (b) (g o f)(0) =…

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Q: Consider the function f(x) = 1 + 2x + 3x² + 4x³. Let s be the sum of all distinct real roots of f(x)…

A: First derivative check for monotonicity

Q: The 2nd approximation to the real root of the equation x³ – x² – 1 in the interval [1, 2] using…

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Q: Let f(x)=√x. By use of the little o notation justify that the linear approximation to f at x0…

A: Given,           f(x) =x

Q: Q. Find the Z trans form of the following functions by using MATLAB. 1. f(k) = (-2)^(k+3) - 8…

A: Ztransform converts a discrete-time signal into a complex frequency-domain representation.

Q: L (7² +9) (2²+4)² x कर

A: Follow the steps.

Q: Prove that f(x)=4x-2^2x has at least one real zero in the interval [1,2] without actually solving…

A: The given data is: Prove that fx=4x-22x has at least one real zero in the interval 1,2 without…

Q: 1. Let f(x)= x on the interval [-7r, 7T. (a) Compute f42, given by 1/2 -T

A: To compute the L^2 norm of the given function, following the definition of the norm