Evaluate the directional derivative Duf (3, 4) if ƒ (x,y) = /æ² + y² and u is the unit V vector in the same direction as (1, -1).

Q: Express the series using sigma notation. -6m – 3m + 0 + 3m + 6m ... 5 23mn – 9m n-1 3mn +9m 5 23mn…

A: Solve the following

Q: Problem 8. If the focus of a parabola is at (0, 4), and the directrix is y=-4, write the equation of…

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Q: Find the general solution of the given variable separable egm atim. dy *+ ay? (2) %3D

A: Given :dydx=e3x2+4y2

Q: Showing all work, use the method of your choice to find the volume of the solid obtained by rotating…

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Q: B. Verify if the relatin O y= xe is a səlution to yl-2y'ty =o. y = eco( 2x) is a solution to…

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Q: 5. IF sin@=5 =E and@inthe first quadrant, find cos

A: We have to find the cos angle

Q: by which criteria?

A: Apologies for the inconvenience. Here is the correct solution.   If a series ∑n=1∞an has either…

Q: (H.W) 1- Solve by choose M this time (2 x y² + 3 x² ) dx + (2 x² y + 4 y³ ) dy = 0 2- Find the…

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Q: Solve 6+ 3+ ニ 2-t-26 3-7++10 +

A: Please refer to the image below

Q: The area bounded by y =3Vx and 2y =3x is revolved about the x-axis. Using cylindrical shell method,…

A: Solve the following

Q: Find the area of the shaded region. y = x² +1 %3D 5 y = x -1 A 23 2. 2/2

A: Given

Q: (a) Find the value of P(?, 4) and P(?, 6) using permutation formula, where ? is the last two digits…

A: Permutation: Permutation:  The permutation is a method of arranging objects in a specific order.…

Q: 33) Find tue ared ef tue Serface formed by revolving thecirele r= f10) = 10 C6s Q f10) =10 Cos Q…

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Q: Find the area of the shaded region. x = -y 2 x = 2 - -2 A B 10 3 2.

A: Given query is to find the area of the shaded region.

Q: Show that g : B → A, g(x) = √ln x is the inverse of f. Why is f^−1(x) 6 ≠ −√ln x?

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Q: The function f(x) = 2x° 39x + 240x – 11 has two critical numbers. The smaller one is x = and the…

A: Topic = Derivative

Q: dy for x'e*y Find dx sin' ( 3x) + In (y) by using implicit differentiation.

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: t3 – 7t2 + 16t –- 12 t4 – 4t3 + 4t² 5. lim t2 w? – 4w + 1 6. lim w-00 3w2 + 7w – 4

A: limt→2t3-7t2+16t-12t4-4t3+4t2

Q: 7. An analyst has found that Tom's Transmissions Company cost function is: C(x) = 40,000 + 500x –…

A: Marginal cost =C'(x)  To maximize or minimize use double deriveative test

Q: The junior class has 50 students. Fifteen students take only French, 5 students take only Latin, and…

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Q: Describe the graph of the equation. r = 7 cos t i - 16 sin i j+k O An ellipse in the planex = 1,…

A: We have to describe the graph of the equation.

Q: Describe the graph of the equation. r= -3 i+tj+(t2-1) k O Itis a parabola in the x = 3 plane, vertex…

A: This is a problem related to parametric equation plotter. Based on the x, y and z value in terms of…

Q: Using (sin x) = cos x and (cos x) = – sin r dr dr Show that # (cot x) = - csc² x dr

A: We need to show that ddx(cot x) = -csc2 x Given ddx(sin x) = cos x and ddx(cos x) = -sin x

Q: -12 1. ("(25x – 46x + 3)dx -12

A: topic- definite integral if f(x) is a odd function∫-aaf(x)=0

Q: Answer the following questions for the function f(x) = x/x? + 1 defined on the interval – 5 <x < 7.…

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Q: Find the equation of each normal of the function f(x) = 1/3x^3 + x^2 + x - 1/3 which is parallel to…

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Q: Find an explicit formula for an. 15) 0, -1, 0, 1, 0, -1, 0, 1, . . .

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Q: TUTOR %3D for the function

A: The given equation is: 4x2+x3y+y2=6...(1) To find the slope, that is dydx, at Q(-1,2)

Q: A plane is given by the equation 5x − 8y + 4z + 9 = 0 a. Find 3 points on the plane b. Find a…

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Q: ry+2 4- (4x2 - ay) dx dy

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Q: The area of the region is. (Type an exact answer, using x as needed.)

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Q: Change the Cartesian integral to polar coordinate | +y*)dx dy

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Q: Problem 11. Solve the following system and express your solutions (if any) as individual ordered…

A: 3x2-2y2=-5     2x2+4y2=18

Q: Question 2 x2 Consider the function f(x) = x² –1 " (a) Find the intercepts of the graph of f (if…

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Q: y x/x, x-4, and y =0 -2

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Q: short

A: Please refer to the image below

Q: 6. The rate of growth of a particular population is given by dp 50t? - 100t3/2, where P is the…

A: Given problem:- The rate of growth of a particular population is given by (dp)/(dt) = 50t2 - 100t3/2…

Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: p.564/ use Trapezoidal method and Simpsons' rule to evaluate.

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 3. Check Euler's Theorem for the function f(x, y) = x + y3 + 3xy2.

A: Euler's Theorem for the function :          x∂f∂x+y∂f∂y = n.f(x,y) ; where , 'n' is the degree of…

Q: long

A: We will use long division method.

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

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Q: find the area of the region bounded by y=(x+2)^2-1, the x-axis, x=-1, and x=2.

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Q: Evaluate the limit 11г3 — 7? — 9х lim 10— 5х — 5а3 I+ 00

A: This question can be solved using the concept of limits.

Q: tdt 1-t4

A: Topic = Integration

Q: Find the sum of the series. 1 - In(4) + (In(4))² _ (In(4))³ 2! 3!

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Q: The three basic trigonometric substitutions are in the table below. Integral Contains Try using…

A: We will solve the integration.

Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

A: Given query is to find the value of the integral.

Q: 3. (D² + 1)y = sec² x tan x. %3D

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Q: In which limits below can we use L'Hospital's Rule? x – 2 lim 1→2 In(3 – æ) 1- et lim 2-0 sin(5x)…

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