1. Find the critical numbers of the function. y = x²+64 Select the correct answer. a) 8,0 b) 8, - 8 c) 64, -64 d) 0,-8 e) 0,-8

Q: Use the Error Bound to find a valve of N for which Error CSN)<1 x 10-9. is 1.5 3x

A: Error bound for Simpson's rule is defined as follows.  For a function fx, if  f4x≤M, then…

Q: Find the line of best fit for x: 2 2 68 10 y: 01233 O ŷ= 0.344x+0.125 %3D O ŷ = 1.29x - 3.14 %3D Oŷ…

A: The regression is a linear relationship between one dependent variable and one or more independent…

Q: 2. Use the inclusion-exclusion principle to find the number of solutions to the equation r+y+: = 19,…

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Q: Determine the solution set of the matric Ax=0 where A= 1 2 3 2 3 4

A: Given the system of equation is AX=0 where

Q: I'm unsure of how to work a problem like this

A: We need to find a 2-degree polynomial having zeroes at

Q: 2. Show that by using MEAN VALUE THEOREM. u-v n >0 1+v2 3 <tan- < and deduce that 25 ww 4

A: First we have to show that v-u1+v2&lt;tan-1v-tan-1u&lt;v-u1+u2 where 0&lt;u&lt;v. Then we will show…

Q: Show that |qbu)|&x + 7元? the closed on interval [-元,T」 fo1 -π2 2くだ gluen that glven gux) for

A: Given g (x) = x +x² To find the maximum value of g(x). We can differentiate the function and equate…

Q: 1. Use the Intermediate Value Theorem to prove that the equation 3x - 4x? = 3 is solvable on the…

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Q: If h(x) — За — — 1, j(x) k(x) = 21x? – 26x – 11 , show - 7x + 11 , and - - - - h(x) · j(x) = k(x).

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Q: Suppose ƒ(1, 2) = 4, ƒx(1, 2) = 5, and ƒy(1, 2) = -3. Find the linear approximation to ƒ at P0(1, 2,…

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Q: 15. Use linear approximation to find v100.8.

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Q: On which interval is the IVP (x sin x)y' + 2y = x +1, y(-5) = 2 guaranteed to have a unique…

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Q: Prove that in the pairs of positive numbers ¤, y for æ² + y° = r the sum a+y is greatest when z = y.…

A: Here we solve the given problem of calculus.

Q: Prove by mathematical induetion. Ine I+2 +2+2 +2° = 2.

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Q: 74. Show that if 0 < x < y, then Vỹ - Vx < Vy – x.

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Q: 6. Use a substitution to find S (x* + 1)" z³dx.

A: Here we use substitution we find∫x4+111x3dxHere we substitute x4+1=du…

Q: 5. What is UF, where F = 0? Prove the correctness of your %3D answer / computation.

A: To find- What is ∪F, where F = ∅? Prove the correctness of your answer/computation.

Q: 8. Show that, for u, v E R³, ||u|| ||| = (u - v)² + ||u x v||².

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Q: Suppose that two nondimensional quantities are exactly A chapter, express the four quantities (A+B),…

A: Given,          A=8.73       3 siginficant figuresB=1.389     4 siginficant figures

Q: Let X and Y be independent and distributed as N(u, 1). Is T = X-Y sufficient?

A: According to factorization theorem, If the likelihood function L(x,θ) can be expressed in the form…

Q: Find all the joint moments m, n and k = 0,1,.... "nk

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Q: QUESTION The minimum value of n required to approximate xedx by composite Trapezoidal rule with an…

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Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

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Q: 20. Let -(). -- (). (). u = w = If au + yv = w. (x, y E R), then a - y = (A) 2/3 (В) —3/2 (C) 3/2…

A: To find  The value of x-y

Q: Use the following graph of ) to estimate the solution(s) of Ax) = 0 for osxS6.28. 3.14 471 6 28 -1-…

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Q: Suppose that U(x; y) = xe' + ysin z, and that x, y and z can be measured with maximum possible…

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Q: 5. Use De Moivre's Theorem to evaluate (1 – V3i)%.

A: Demoivre's Theorem

Q: Let f be q functiom that admits contırous second partial denvatives Df (X.Y)=(4x²- 2q²x+ 2q°y ,4y³ +…

A: Given, the second partial derivatives              ∇f(x, y)=4x3-2a2x+2a2y,  4y3+2a2x-2a2ywith a&gt;0

Q: 14 11 " f(2)da - /" f(=)dz = [ f(=)dz where a = and b = Question Help: D Post to forum

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Q: Use the difinition of error function Prove that: 5(1/₂/2) = 5T let: ere (x) = 33/3324 dt

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Q: Четверг show that the inu of a bounded E tix-oy ne 7 8. use T

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Q: 3. Suppose that f(1) = 2, f(4) 7, f'(1) 5, f'(4) = 3, and f" is continu- %3D | af" (x) da. ous. Find…

A: The given data is: f1=2f4=7f'1=5f'4=3  f'' is continuous  To find the value of ∫14xf''xdx.

Q: Suppose v(t) = 6t² - 3t on the interval [3, 5]. What is the displacement on [3, 5]? O 160 O 165 O…

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Q: Find the indico 6. 2. 3+ 2 1..2+4+8+ 27 t. 4. 3. 12, (4)"- n= %3D1 2.

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Q: 9:Find the absolute exlemum Verlues of flx) x²-4x+24 over the interNal Cl,41

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Q: • Verify that 3r is a one-parameter family of solutions of the DE ry + y = 3r. • Deduce a solution…

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Q: 1. A bowl contains 10 red and 10 yellow balls, how many balls must be selected to ensure 5 yellow…

A: To solve this type of questions we consider the worst case that is  after taking all red balls we…

Q: Find all the joint moments m,1, n and k= 0, 1. . .

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Q: Solve the BVP on interval Lo, nJ) 2 %3D 2.

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Q: prove with a table if x → y then xor y xor y = y

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: 2) Prove by using the pigeonhole principle that among any 17 points in a square of side one there is…

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Q: Show that if ƒ′′&gt; 0 throughout an interval [a, b], then ƒ′ has at most one zero in [a, b] . What…

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Q: Suppose that U(x; y) = xe' + ysin z, and that x, y and z can be measured with maximuma possible…

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Q: Use cubic interpolation method with two points to find uz , where a = 0. 6, h 0.1, ɛ = 0.001 and O'…

A: Cubic interpolation method gives the following formula for evaluation, For, μ2=a(∅')-h1+∈ Therefore,…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.