Find the derivative. Ni at

Q: 15r If F(r) = and o is the surface (r – 3)? + y +z? = 49 oriented outwards, what is the value of F n…

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Q: Describe the graph of the equation x2 + 4x – 16y + 36 = 0. -

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Q: Evaluate CF dralong the line segment C from P to Q. F= x j; P(3,2), Q(3,8) SCF dr- i

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Q: Water is pouring into the conical vessel 15 cm deep and having a radius of 3.75 cm across the top.…

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Q: Consider the solid obtained by rotating the region bounded by the given curves about the X-axis. y…

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Q: 1. [5.1] Determine the equation of a line tangent to the curve of x = 1. f(x) = 5e* +1 at 2. [5.1]…

A: A detailed solution is given below

Q: Klara is building a fence in her backyard. The sides of the fence will form a right triangle with…

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Q: 00 1 dx x(Inx)2

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Q: Use Green's Theorem to evaluate the integral (3x² – y)dx + 3xdy where C is the circle a? + y? = 1…

A: As we know from the Green's theorem; ∫CMdx+Ndy=∫∫D∂N∂x-∂M∂ydA   Given; I=∫C3x2-ydx+3xdy So, M=3x2-y…

Q: Determine whether F(x, y) = 2x²y i+ 8xy' j is a conservative vector field. If so, find a potential…

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Q: Solve the initial value problems: y^ prime =6+5y+y^ 2 ; y(0) = 0

A: We need to solve D.E.

Q: The distance a biker has traveled after t seconds can be modeled by f(t) feet and f(50) = 64. f'(t)…

A: f'(t) > 0 imply function increase with time.  f"(t)< 0 imply function is concave downward

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. dy

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Q: |(sin5 (x)) dx

A: Given ∫sin5x dx

Q: aph the function g(x) = x* + 2, if x < 1 Is the function continuous? Explain. x +2, if x 2 1

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Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use dx x(In(x?))5

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Q: Q1/ Find the volume of the solid generated by revolving the region bounded by y = Vcos x, y 0 & Osxs…

A: Disk method: The disk method is used to find the volume of a solid when the axis of revolution is…

Q: csc z) Evaluate: lim (x² + e¬®)@¯

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Q: Theorem to find the flux of "(x, Y, z) = x°i + y³j+ z°k f the cylindrical solid bounded by x² + y?:…

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Q: 4. x = VI - i , y = t³ – 3t

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Q: Clairaut's Theorem Let DCR be a disk containing the origin and assume that g: D→R is a function…

A: Given

Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: We have to solve above question

Q: Let f(x) = Va (2 – x)2. Use the local linear approximation of f (x) at ro V0.99 (1.01)?. 1 to…

A: To use the linear approximation for the given function

Q: Let fa)=S(-5-x2 + 23x +19 f Xチー6 if X= -6 calculate the following limits. ENter DNE if the liniit…

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Q: Y201003 2. b00 Cos07 30 300 Sing Y=0.002 Ysine dr dodø

A: Given

Q: H.W: 1. Find the area of the region inside the oval limacon r = 4 +2 cos 0 2. Find the area of the…

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Q: Evaluate the definite integral. Si f (æ) dæ, ƒ (x) =47–(7x³+ 13)/x?

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: H.W: Use the comparison test to determine the following series converge or diverge: 1 3" +5 n=1

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Q: A theatre has a seating capacity of 250. The ticket prices for children and adults are $8.00 and…

A: Let 'x' be the number of  children's and 'y' be the number of adults. Now x≥0 and y≥0 since the…

Q: Use Green's theorem to calculate.(2x³ – y*)dx + (x³ +y*)dy, where C is the boundary of the annular…

A: Apply greens theorem

Q: Find T(t) and N(t) at the given point. r(t) = 10 cos(t)i + 10 sin(t)j + tk; t = 2 TE) -| 6) =

A: we have to find unit tangent vector and normal vector.

Q: (a) Put a pair of brackets on the left hand side to make these statements correct. 17-2 + 8-4- 11 -…

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: I really need your help, just want a guide or like a script type how to explain this on class each…

A: Here, you have to find the area bounded by the loop of the given curve. The given curve is: y2=x5-x2

Q: 3 5) Differentiate with respect to x: y = %3D 3x e

A: Solving the problem by finding the differentiation.

Q: Given the Total Cost function, TC = 10 + 5Q?, find the marginal cost function, MC when Q = 10. [2]

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Q: A2. (a) (i) Find the future value of £2000 when it grows at an annually compounded rate of 5% for 10…

A: To find the future value of £2000 when it grows at an annually compounded rate of 5% for 10 years.…

Q: Consider the plane curve given by the parametric equations x = t + 22t – 23 y = t2 + 22t – 5 -- What…

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Q: Evaluate the double integral over the rectangular region R.R. ∬R7xy3dA;∬R7xy3d⁢A⁢; R={(x,y):…

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Q: Using the graph of two functions f(x) and g(x) on the right, find: a.f(g(2)) b. g(f(−1)) c.…

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Q: Use the principle of mathematical induction to show that the given statement is true for all natural…

A: Question number 6 has been solved as per the requirement of the student.   This question can be…

Q: Q6. Identify the incorrect statement in the following: A. If e* = 2 then x = ln 2. B. If In x = 2…

A: Find your answer below

Q: Which of these statements is False? А. (а?)3 — а6 Вв. а?а — а = a' a2 C. a3 = a-1 D. a? + a³ = a°

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Q: An Easter ham is put in the oven with a temperature probe embedded in the center. Assume the…

A: We are given that, an Easter ham whose temperature is 40° is kept in an ovan whose temperature is…

Q: Verify Green's Theorem by evaluating both integrals v² dx + x² dy = / / dA ax for the given path. C:…

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Q: Use Green's Theorem to evaluate the line integral (y – x) dx + (2x – y) dy for the given path. = x²…

A: Green's Theorem: By Green's Theorem we have for a differentiable function f(x,y)=M(x,y)+N(x,y) and a…

Q: dy 1. Find for the following: dr :b. y sin y = ry

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 3 1 lim tto0 2t2 +3' 2t (?,?)

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Q: Question 2 A balloon is rising vertically over a point A on the ground at the rate of 15 feet per…

A: Using differentiation