1 What is the direction of fastest increase at (-3, 4, –4) for the function f(x, y, z) = x2 + y2 + z2° (Use symbolic notation and fractions where needed. Give your answer in the form (*, *, *).)

Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

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Q: c) Use Secant Method to find the root of f(x)= x -x-1 with two initial points x, = 1 and=1.5 and =…

A: Secant method Steps  Step-1: Find points x0 and x1 such that x0<x1 and f(x0)⋅f(x1)<0.…

Q: .2 2 4) Let f(x) = xe²-z*". Find the following: a. Critical numbers b. Intervals of increase and…

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Q: 22. The function f(x) = Vx – 6 is transformed according to (x, y) → (7x – 7, - y+1). the transformed…

A: Substitute fx for y in the transformation and simplify. x,y=x,f(x)→7x-7,-f(x)+1=7x-7,-x-6+1

Q: 1/4 using the Linear Approximation L(x) of f(x) x14 at a = 16 Approximate 181/4 (Use symbolic…

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Q: What is/are the critical number(s) of the function S(2) = +4, f(z) :

A: f(x)=x2+4xDifferentiatef'(x)=x2x-x2-4x2f'(x)=2x2-x2-4x2f'(x)=x2-4x2

Q: Find the critical numbers of the function: f(x) = x3 - 3x2 +1 %3D | Select one: а. X-0, х32 b. x=…

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Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A: Given: f(x) = x − 6/x satisfy the conclusion of Mean value theorem in the interval [1, 3].

Q: 2. If :|S1, determine the maximum modulus f(:) (a) f(=) =z-2z+3, (b) f(=) == +z-1, (c) f(=)3= :+1…

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Q: Find the linearization of y = eV3x at x = 64. (Use symbolic notation and fractions where needed.)…

A: Solution: The objective is to find linearization of the given function

Q: 14. Suppose that Yk+2 – Yk+1 + 2yk = 4*, k > 0, and that yo = 2, y1 = 1. Find yk using the method of…

A: Solution of difference equation is a function that satisfies the given difference equation. Solution…

Q: 18. Solve for A and B so that f(x) has a limit at both x = 2 and x = 4. 3x + 4, x> 4 f(x) Ах + B,…

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Q: Find the linearization of y = eV1x at x = 36. (Use symbolic notation and fractions where needed.)…

A: We have to find linearisation

Q: f(6) = 2sece+ tan@ 6 <8<8| %3D 7. Find all critical numbers of of the function

A: We have to find critical numbers for given function:

Q: 5. Suppose that f (x) dx = = 5, f (x) dx = -3, g(x) dx = -1, and g(x) dx = 2. Compute | (2f(2) –…

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Q: Which one is one of the critical points of the function f(x, y) = 2x + 2y + 8x - 4y + 11? Select…

A: Solution is given below:

Q: 6. Find the Wronskian for the set of functions {e¬x, xe¯*, (x + 1)e¬*}.

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: for f'(x) see 2nd and 3rd step. for g'(x) see 4th and 5th step.

Q: Q-2: For what values of a, m and b does the function: 3, f(x) = -x² + 3x + a, 0<x <1. (mx + b, 1<x<…

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Q: 11. Find the absolute minimum and maximum of f(x) = r3 - 4x2 - 3x + 3 on the interval [0, 4].…

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Q: b. By choosing a small enough value for h, you can estimate f' (a) with arbitrary precision by…

A: Lets do part B Given information : f(x)=2xf'(x)=f(a+h)-f(a-h)2h we need to find f'(0) when…

Q: Find the value of “c” guaranteed by the MVT theorem over the interval [-8,-6] for the function: F(x)…

A: Given function is : Fx=2x3+9x2-60x        -8,-6 To find the value of c.

Q: e. y= (x² + 4)/x in the interval 1<x<4. 8+ 4ln4 - % s.u ans.

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Q: convcrges for all r. n! n=1 Σ 24. Show that

A: To show the series∑n=1∞rnn! is convergent for all r; ratio test can be used. Ratio test rules that…

Q: Find all the critical points for the function f(x, y) = x² + 8xy + 4y² +3. (Use symbolic notation…

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Q: 9. Find the local and absolute extreme values on k(x)=(x-2)° +3 on | the interval [0,5].

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Q: 00 n + 1 is divergent. If we multiply any constant (labeled as h)to the n + 1 such that n + 2 n=1 n…

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Q: 12. Find the general solution using Reduction of Order: a) y"= 2ln x b) y" + y' = cos 3x

A: We have to find the general solution: y''=2lnx. Here, the value of y1 is not given.

Q: 5. Show that the formula for the Secant method can be written in the form xn+1 = [f(xn)xn-1…

A: Secant Method: Consider, y = f (x). Let, x0 and x1 are two initial approximations for the roots of f…

Q: i) Estimate (2.03)' with f(x)= -2x° by using the linear approximation. ii)Estimate In( 1.03) by…

A: Dear student we are allow to solve first question only if you need rest of answere please upload…

Q: and X4 %3D If the engine type is traditional, then x3 = When you plug in these two values in the…

A: When the qualitative predictor has m levels then we create (m-1) dummy variables. Here the…

Q: 84. Let f(x) = x' +3x² - 24x + 1 and g(x) =x' + 6x² - 36x + 1 . For what value(s) of x do both f(x)…

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Q: 1. Consider function f(x,y) for which = 24x² + 114y and %= 114x + 24y2. Wbich of the points (5, 5)…

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

Q: a.) On the interval (-o, 0), f"() b.) On the interval (0, 0), f"(x) = Thus, c.) On the interval (-o,…

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Q: 2 The function f(x)= (x² – 1) ³ , is decreasing on the interval (- 00,-2)U (0,2) AO (-1,0) U (1, ∞ )…

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Q: 1. If Jis any subinterval of [a, b] and if ø,(x) := 1 for x E J and 4,(x) := 0 elsewhere on [a, b],…

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Q: 4. Find the absolute max and min of f(r) = 2+5x - x* on the interval [0, 4 ]

A: Calculate the value of function at local extremum point and end points of interval.

Q: If X1~N(H1,0) ,X2~N(H2,0 are X2 independent then the marginal of X2-H -1/2(- 02 1 is given byf(x2):…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 12. Suppose we know that f (x) is continuous and differentiable on the interval [1,9], that f (9) =…

A: To find: The largest possible value of f1. Given: The fx is continuous and differentiable on the…

Q: 11. [D' +4]y=sinx, using reduction of order and letting y, = vcos2x. (Note: This is the same problem…

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Q: 50. Suppose that in approximating a zero of f by the Newton- Raphson method we find that f(c,) =0…

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Q: Consider the function f(x) = 9x + 4x-1. For this function there are four important intervals: (- 00,…

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Q: Find the absolute maximum and minimum values of f(x) =z-3x2 +2 nterval -1, 1]. Hint: be sure to…

A: Given query is to find the absolute maximum and minimum for f(x).

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: We use the quotient rule, product rule, and chain rule of differentiation to check the claim of the…

Q: Find the critical numbers of the function f(z) = 2z'- 3z² – 36z. Answer (separate by commas): I =…

A: Given f(x)=2x3 - 3x2 - 36x and we have to find out critical numbers

Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

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Q: Suppose X- N(H, 36 ) and P( X > 6 ) = 0.13. Determine the value of u. (Give your answer to 4 decimal…

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Q: 8. x' + 10x² + 6x + 4 is concave down. 3 Determine the interval(s) at which f(x) = -- a) O(-1, 00)…

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Q: Consider the function f(x) = 12x + 45x4 – 200x³ + 5. For this - function there are four important…

A: The given function is: fx=12x5+45x4-200x3+5 To find the critical points of this function, first,…

Q: Find the linearization of y = eV3x у at x = 64. (Use symbolic notation and fractions where needed.)…

A: topic- linearization of a function