1. Integrate the following functions over th given interval by using the extended trapezoidal rule with intervals of N= 2, 4, and 8 a. 3 X3 + 5X - 1 [0,1] b. Tan X [0 , t/4 ] et [0,1] C.

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A: Given, a decreasing concave up function f(x) on the interval 2, 5 with f(2)=10,  f(5)=3, f'(2)=-4,…

Q: If m < f(x) < M for a < x < b, where m is the absolute minimum and M is the absolute maximum of f on…

A: Smaller value 0.4363 Larger value 0.7557

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Q: Which of the following functions of x is guaranteed by the Extreme Value Theorem to have an absolute…

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Q: 1. Find if the function is continuous in the given points (sin(x+y) x+y 1 D) f(x, y) = x + y = 0…

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Q: Which of the following functions of x is guaranteed by the Extreme Value Theorem to have an absolute…

A: Option (C) is correct. Because the given function is continuous in the interval [0 4].

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Q: If m≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: hoaph fumeten nd be fure at label aut least thne f (u) : Su

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Q: 1. Integrate the following functions over the given interval by using the extended trapezoidal rule…

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Q: I don't understant this hw problem

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Q: 3 B Consider the following function, z= x -2xyty't yn Lind the alues of ag Ddz,z,when redgyel dy 6.

A: Given : z = x2 -2xy + y3 + yw

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A: We need to find the first two intervals of on the interval

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Q: 300r Integrate numerically: f (x) = 1+e from 0 to 10 using 5-segment trapezoidal rule. Round-off the…

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Q: Consider the following functions. f(x) g(x) = 8 sin x = 8 cos 2x 6 Sketch the region bounded by the…

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Q: Tind the limits sin(t) i+ lim In(sin(t)) In(tan(4t)) -j+tln(t) k| = t+0 sin(4t) 1 t2 – 5t + 4 lim…

A: Explanation of the solution is given below...

Q: Given a decreasing concave up function f(x) on the interval [2, 5] with f(2)=10, f(5)=3, f'(2)=-4,…

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Q: is continuous and integral 3 to 1 f(x)dx =8, show that the graph of f intersects the line y=4 at…

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Q: 12. Let f(x, y) = tan(ry). Find f, and fy for this function.

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Q: Let z be defined implicitly as a function of x and y by the equation dz 4+ In (xy²) – cos (xy – z) =…

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Q: Find the arclength of the following function from x = 0 to x = 2 (x² +2)Wx² +2 f(x)=. 3

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Q: 1. Evaluate the following integral: (6 + 3 cos x) dx a. Analytically b. single application of the…

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Q: If m < f(x) < M for a < x < b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: 2. Set up an integral to find the exact length of the curve defined by 1 f(x) = 1 In r 2 - 4* where…

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Q: The modified Bessel function I,6x) has the integral representation /2 2 1(x) = cosh(x sin 0 )d0. Use…

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Q: a non zero valie for the constant k that makes the fmction ww m tan(kx) x< 0 f(x) = 3x + 2k?, x 20…

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Q: 1. Prove: a. csch x In +c %3D b. sech x = 2 Arctan(e*) + c %3D

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Q: 12) a) Use either the Trapezoid OR Midpoint Rule to estimate [ In(1+e* ) dx using at least four…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: If m≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on…

A: we have to find the smaller value and larger value

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Q: Find the smallest value of n such that the remainder estimate |RI s M (x - a)" +1, where M is the…

A: Given: f(x) =sinx