Consider the integral 1 ∞ y(t) = — _ x(7)[5(7 − 3) + 6(7 + 3)]dr, y(t) can be 6 8 simplified to:

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

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Q: Use algebraic manipulation to prove that (X +Y)(X + Y) = X

A: Given: X+YX+Y=X Now, first we shall simplify left hand side of equation.

Q: The set of zeros of f(x) = x³ + 4x² + 4x is (B) {0, -2} (C) {0, 2} (D) {2} (A){-2}

A: find the zeros of the function fx=x3+4x2+4x

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: a. Let f(x) = (-4x² + 3) (-4x² − 3). - Then f'(x) = b. Let g(x) = 2√√x + 3 x4 +2x² Then g'(x) Hint:…

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Q: Find all functions y satisfying y" + y" = y' + y. You may use the factor- ization x + x² – x - 1 =…

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Q: 2) Determine the root of f(x) = x³ – 9x² + 3.8197 = 0

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Q: If f(x) In - In( + o). + e6x, find f (0).

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Q: Determine a value for m so that h (x) = -1/3 x^3 + nx^2 + 8x – 15 has an inflection point at  x = –…

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Q: 3.) flx) x+2

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Q: Determine the number of roots of the equation f(x) = In|x + 2x^2 - 5x + 1a for all real numbers a. -

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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: attached

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

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Q: 4. Find the zeros of f(x) = x² + x – 3.

A: We know that, for a quadratic function fx=ax2+bx+c, the zeros of of fx is given as x=-b±b2-4ac2a…

Q: nsider the following. -2x5 + 9x4-7x³ - 12x = 0, [3,4] ) Explain how we know that the given equation…

A: In this question, we will find the solution of the equation.

Q: (3x²-x+4)(x² + 2x - 1) 2

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Q: Show that f(x) = x4 + 4.x + c has at most two real roots for any umber c.

A: Consider the given equation. fx=x4+4x+c Case 1: When c>0. No sign change, by Descartes rule of…

Q: Give the domain of s(x)=x2+2x√16−5xs(x)=x2+2x16-5x in interval notation

A: Given the functions(x)=x2+2x16−5x

Q: dz √|z|=1 |z|=1 z²-8z_+1

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

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Q: 6. (x – 1

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Q: Express ƒ(z) = 4x² + i4y² by a formula involving the variables z and ž.

A: Let,

Q: For j(x)=(3x2−6x+10)(x3), find j′(x) by applying the product rule.  Do not include "j′(x)=" in your…

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Q: Show that: n n > (xi – x)2 > x? – n(x)2 | i=1 i=1

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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: Q3) prove that: fa+¹h f(x).dx h 2h 4h - = 3 [ƒ (a) + f(a + 4h)] + f(a+2h) + [f(a+h) + f(a + 3h)] 3 3

A: Introduction: Numerical integration is a word utilized in evaluation to explain a set of strategies…

Q: In (2x2+x) V 34*(3x4+2x-1)5 3 f'(x) if f(x): ||

A: Topic - derivative using logarithmic

Q: -Vx2+5 -x f(x): f'(0)? -x+2

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Q: Indicate the answer choice that best completes the statement or answers the question 118 59 13 Oa.…

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Q: 2. Lim (3x+6x -8)

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Q: ७) Let యర with Aand be commutetive Xing that that 1of iniby Then Such Poove ২ A.B AnB

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Q: 5 Evaluate [ (x + 2)(x² - 1) dx

A: Solution:Given   let      I=∫25(x+2)(x2-1)dxFormula:∫xndx=xn+1n+1+C