| 45. Apply integration to the expansion 00 =E(-1)"x" = 1- x+x – x +.. 1+x n=0 to prove that for -1

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Q: 4. The function A(t) = 2000(1.)' represents the growth of algae in a pound after time t (in hours).…

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Q: 10. Let [ A= 103 -1 21 02 Calculate det (A) by cofactor expansion.

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Q: 33. Given the function, defined in the range [0, 1], find the function P(x) defined in the ra [0,]…

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Q: Q1. Find an approximation to the root of f (x) = e¬* – x using 4 steps Bisection Algorithm

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Q: Suppose f"(x) = N;(h) + a,h* + a;h® + azh® + ... When calculating N,(h) using Richardson…

A: Solution

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A: Topic: differentiation

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Q: 3dx x(x+3) D. Evaluate :

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Q: + 2x Compute dæ. O 3(z+z²) +C 1 1. I미 피 + C 2 O x +2 ln |æ|+C

A: Given: I=∫1+2xx2dx

Q: Which of the following does not satisfy the conditions of the Mean Value Theorem? Select one: O a.…

A: We recall the theorem and then proceed to sovle the problem

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A: Given P(x)=a(b-x)(x+c)(dx+1) 1st term of expansion=-8x3 P(-3)=0

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Q: 6. For positive integer n, prove the following (given that I(½) = √√): √π = (2n)! √T. 4nn! T(n +…

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Q: 17. Let P1.Pn be positive real numbers such that P1+ + Pn=1. (a) Prove the following: @P² ≥ (ii)…

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Q: dx_ -In x – 2 |x+2 X - + C x² – 4 - 4 Select one: O True O False

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Q: 33. Given the function, defined in the range [0, 1], find the function P(x) defined in the range…

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Q: 57. Use the substitution u = x/3 to prove dx 1942=tan 1+0 www C 9+x² 3 3

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Q: 3. (a) Find a unit in Z[√2] which is not equal to 1 or -1. Hint: Use 1 (b). (b) (*) Show that Z[√2]…

A: The objective of the question is two-fold. First, we need to find a unit in the ring Z[sqrt(2)] that…

Q: 4x + 4 -dx. Choose all of the following that are correct. x² + 1 Consider the definite integral

A: To evaluate: ∫014x+4x2+1 dx Solution: We know that, ∫f'xfxdx=lnfx+C ∫1x2+a2dx=1atan-1xa+C

Q: 8. [8] What is the coefficient of y* in the expansion of (3y-2)'.

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Q: If X~ Uniform(b, 1) and o² = 3μz, what is b? (a) -0.82 (b) 12.18 (c) 20.82 (d) 17.00 (e) None of the…

A: To find the value of&amp;nbsp;b, we first need to find expressions for the mean μX​ and…

Q: 4. Show that the function log(1+ x) lies between functions x - and x for all x > 0. (Hint 2(1+ x)…

A: We will expand log(1+x) by Maclaurin's series. Let f(x) = log(1+x)

Q: 2. Evaluate L-T/2(-1-i√3)

A: To evaluate the expression L base-pi/2[(-1-i√3)], we need to first understand what this expression…

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A: Write integral as limit of a sum.

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Q: -2x xp- (1-x)' 7. Evaluate A. +6x-n(1-x)+-(1-x)* +C C. '+6x + n(1-x)' + (1-x)*+c D. x+6x + In(1-x)"…

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Q: Show that x+1/x is increasing on [1,∞]

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Q: k* for some constant k". Lp.) Show that L(po)

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Q: 14. Let f(n) = n² + 20 and g(n) = n³. Show that f(n) is O(g(n)) by finding a positive integer N for…

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Q: Q2/B/ check the function continuity at x-0, for the fimction f(x)%= 1+ 4 2/3

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