64 Use the first derivative test to answer the following: the function f(x) = 49x + I and a local minimum at r= at x = has a local maximum

Q: z²i+xzj+ye² of the sphere x² + y² + z² Given F = 2 [[ S 50 that lies inside the cone z = √x² + y²…

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Q: Constraint 1. V= 32000 cm³ xyz = 32000 g(x, y, z)=xyz-32000 vg = (y², xz, xy) function SA= xy + 2yz…

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Q: 1 g(x)= {x-1 if x > 0 |x² −1 if x≤0

A: The given function, gx=1x-1if x>0x2-1if x≤0

Q: 2 Solve the following ODES by Inverse Operator method. (D²³+1) y = 3+²+52x Ans: y = c₁e²+ ¹² (C₂…

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Q: The integrating factor of the given DE are already given below. What is the value of “n” y2dx…

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Q: is 2 Sinh xt sinh (۱) Let y emx (to) be the trial solution to the Corresponding homogeneous equation…

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Q: What is the directional derivative of f(x, y, z)= In x 2 + 2y2 + 4 z 2 at the point P(-1. 2, 4) in…

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Q: Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule. Compare these…

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Q: Match the following iterns for the integral of (12) Using partial fractions, the above integral has…

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Q: [² (8cx² = 6cx+6c) de Identify the variable of integration in the given definite integral. Type only…

A: Given problem:- ∫pq8cx2-6cx+6cdc

Q: 9) 1 What value(s) of x makes + ed 0.91/14 4|33|4 b. 0, X x+4 = 2 true? C. d. 2√√3 3 3

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Q: Cut out squares (of the same size) from the four corners of a square cardboard of given side length…

A: The side of the square = L  let the length of the square = x,

Q: Evaluate the following definite integral by using suitable trigonometry substitution: √2√3-2² dx.

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Q: Solve 4 sin x = 1.35,3.65 x = 3 for the four smallest positive solutions Give your answers accurate…

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Q: the particular Solution is 1 84-1 2. = 2. 1 04-1 — (ex) - 1/₂₁ (2x), D4-1 = LYDB (ex) = 4p3 De_…

A: Given D4-1y=2 sinhx+sinx The auxiliary equation is m4-1=0⇒m22-12=0⇒m2-1(m2+1)=0 Therefore m= ±1, ±i…

Q: 5. [tan³x sec³x dx

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Q: You go to the doctor and he gives you 14 milligrams of radioactive dye. After 12 minutes, 6.5…

A: Given ,  You go to the doctor and he gives you 14 milligrams of radioactive dye. After 12 minutes,…

Q: lim X+0 2-√ 4-X² x ²

A: We can find the answer by finding the limit as below.

Q: Given the function f(x, y) = e5-2x+3y, approximate f(4.1, 0.9) using point (4,1) for (xo, yo). What…

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Q: The function is not one-to-one. Delete part of the domain so that the function that remains is…

A: Here we have to find the inverse function.

Q: y(2xy +1) dx + x (1 +2xy - x³y³) dy = 0

A: See this solution in below

Q: Write the given differential equation in the form L(y)- 90x), where L is a linear 4y"-15y4ys…

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Q: Use Properties of Exponents and Properties of Logarithms to simplify and the following expression…

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Q: gas station stands at the intersection of a north-south and east-west road. A police car is…

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Q: Write the expression in algebraic form. [Hint: Sketch a right triangle, as demonstrated In Example…

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Q: 5. 6. Je*cos2x dx dx 3 (x+2)4 -(x + 2)2 S-

A: I have stated the used formulas in the solution

Q: the function, do the following. f(x) = 2x  from  a = 3  to  b = 4   (a) Approximate the area under…

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Q: 2 (D² +8D³² +16) y = - sinx Ans: Y = C₁ cus2x+ C₂ Sin2x + C3 Xcos2x + C4 X sinex-_-_sing

A: Solution of given question is written in below steps.

Q: Use the one-to-one property of logarithms to solve. (Enter your answers as a comma-separated list.)…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: A local club is arranging a charter flight to Hawaii. The cost of the trip is $543 each for 83…

A: We need to find no. of passengers and max. revenue.

Q: Solve the given differential equation by undetermined coefficients. y" - 8y' + 16y = 12x + 6 y(x) =

A: The given differential equation is;  y''-8y'+16y=12x+6.

Q: 1. S sina de cos²x

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Q: Evaluate the function for the given value of x. r(x)=3x, p(x)=x2+6x,(p-r)(x)

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Q: 10. 2ste tds +(s²e-t - t)dt = 0

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Q: . Find the open interval(s) on which the function is increasing and decreasing.

A: Given :f(x)=9x3-11x

Q: 1. Set up the formulation to find the surface generated when the curve y = x² is revolved about the…

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Q: Let f(x)=√/25 - x The slope of the tangent line to the graph of f(x) at the point (9, 4) is The…

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Q: To integrate by u-substitution, which part of the integrand should you choose as u? S cos de sin² x…

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Q: 2 Determine the length of the curve = = t³, y: 31² 2,0 ≤t≤ √3.

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z)=√√√√x² + y² + z² (4,…

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Q: If In a = 2, ln b = 3, and ln c = 5, evaluate the following: a² b²c4 (a) In = (b) In √a²b²c4 =

A: To evaluate the given expression.

Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

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Q: The holes cut in a roof for vent pipes require elliptical templates. A formula for determining the…

A: We need to find length and width.

Q: f(x) =  5 x2 + 6 Describe the interval(s) on which the function is continuous. (Enter your answer…

A: Polynomial function are continuous every where so using this we solve this problem

Q: y'(x) = 49e²7 -46₂2642 де +2.4e4x + 9.6ne 422 -4 HOW DID HE GET THE VALUE INSIDE THE CIRCLE, CAN YOU…

A: We need to find y'(x).

Q: 9 P cost D2 + 1 }; రె 2 cos²x T+a {

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Q: Using the circular disk method, find the volume of the solid generated by revolving about the…

A: Given curves , y=x ,                   (1)x=4.                       (2)

Q: The graph below is the function f(x) -5-4-3-2-1 Find lim 24-1- Find lim 2 1 02 03- -4- 4 z→-1+ Find…

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Q: Solve the following ODES by Undetermined Coef D Ş 17 4X y - 16 y = 19.2 e + 60e, y(a) =ý (os. 4X -4X…

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