9. Jer'y ds, C:x cos t, y sin 1, z = 1, 0<1s/2 %3D 77

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = xy + yz + zx, Po(3, - 3,…

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Q: Let R be the finite region enclosed by the curve y = 6x(3 – 2x) and the x-axis. Let V be the volume…

A: See the solution in below

Q: dz dz and ду IV. Suppose z is a function of x and y, and tan Vy? + x² = z"e©y. Solve for

A: We have to Solve as per given conditions.

Q: inst /3. 2x2 + 3x, where both z and x are both functions Suppose that z = 9x Given that x is…

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Q: 2r 2r If the total volume of the cylinder and square block is 30 cm', express h in terms of r.

A: Given that total volume Volume of cylinder+volume of cuboid=30 πr^2 ×h + 2r ×2r ×r =30 πr^2 × h…

Q: . Use L'Hospitalľ's Rule to evaluate lim t In 1+

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Q: Pr. #3) Prove that the limit does not exist. cos(4ry)- 1 lim (x.v)-(0,0) 2r + 3y4

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Q: Suppose f(x) = ex, xE[0, 1]. (a) Find the slope of the secant line connecting the points (x, y) =…

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Q: 1 an 1 Use the transformation u = 2x+ y, v=x+ 3y to evaluate the given integral for the region R…

A: Given

Q: A particle started to move from the origin along a curve with velocity given by the function Cos T…

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Q: What are the local extreme values of the function f(x) = x' – 3x + 2? a. None of these. O b. Local…

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Q: Using concepts from this unit, Curve Sketching, of this course only, explain why a quadratic…

A: To explain the correct reason.

Q: How to solve for the derivative of Dy[tan(y)+1/tan(y)-1]? If it's 0, why?

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Q: Using the definition of differentiation, find the value of f'(a) if f(x) = sinx

A: Topic = Derivative

Q: 2x y= Arccos(e)

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Q: Given the function f (x) = %3D x - 4 Find the interval where f (x) is increasing or decreasi

A: Given: f(x)=xx-4

Q: az Find əx if yz – In z = x + y -

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Q: ppose a compa headsets, the cost and revenue functions (both in dollars) are given by C(x) = 32,000…

A: Profit = revenue - cost Px=130x-0.001x2-32000+60x=-0.001x2+70x-32000

Q: (80") (7")(9") + 1* n=1 IM:

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Q: Evauate: |(*+xy) dx+ Cy- xy)dy; C: the x-axis from the origin to 2,0) and then line x-2 from (2,07…

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = e 2x2 + y? - 8x…

A: To find out all the local maximum, local minimum and saddle points.

Q: If on V = R² define the usual scalar multiplication « (x, y) = (« x,x y) , and addition (x1, Y1) +…

A: Concept: Vector space: Vector space is defined by the associative and commutative laws of vector…

Q: V9 – x² x2

A: Given: I=∫9-x2x2dx   ...1   As we know that; The trigonometric identities; 1). sin2x+cos2x=1 2).…

Q: dz dz Draw a dependency diagram and write a chain rule formula for and given the functions below. ds…

A: 1. D  2. D

Q: A particle is moving along a horizontal path which starts at a distance of 5 ft to the right of a…

A: Let's find.

Q: (iii) Extremum point(s), (iv) The interval of concavity, (v) Inflection point.

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Q: 24 – 49 dy 2+ 49

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Q: -2 Sx'V4 – x²dx

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Q: Identify a generating curve on the rz-plane for the surface of revolution with equation 1² + y³ + z²…

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Q: (b) 2+ 5y = 2, y(0) = 0 dt

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: iv. L, x* (e* – e*) dx

A: Given:

Q: Question 5 The approximate value of -31.8 using linear approximation, imaginary O (E) None of the…

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Q: tution for each of the following indefinite integrals. To input inverse trigonometric functions use…

A: We have to substitution

Q: ladder away

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Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. (n +…

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Q: 2у — 4 dy 2 + 49 с.

A: To evaluate: I=∫2y-4y2y+2dy=-∫4y-2y2y+2dy=-∫22y-2y2y+2dy=-∫2y-12y+22ydy=-1ln 2∫2y-12y+22yln 2dy

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. -…

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Q: Given f(x) = (2x - 3)" (x+1). Determine (if any)

A: Given

Q: Describe the end behavior of the graph of the function f (x) = 5(4)" - 10. For o, type in the word…

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Q: Find the total differential du. 1. w = y tan a? – 2xy

A: To find the total derivative

Q: 2r 2r If the total volume of the cylinder and square block is 30 cm', express h in terms of r.

A:

Q: (in) S 15:22 15-z dx. u = (M S 15 - TV9 – a² dx. u= (vi) S dr. u = 22+15

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Q: 04: S+* + 1)sin z dz =

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Q: y to find the derivatives of the following functions before we continue. a. F(x) = x³ + 2x2 + x b.…

A: a) F'(x) = 3x2 +4x +1  b) F'(x) = 3x2 +2x +1  c) F'(x) = 9x2+3

Q: 1. Evaluate the following integrals. | (csc 0)(1 + sin² 0 + sin 0 cot? 0) de а.

A: Given ∫(cscθ)(1+sin2θ+sinθcot2θ) dθTo evaluate the integral:

Q: If a, ß be the roots of m (x-x)+ 2mx +3 = Q and m,m, be the two values of m for which a, B are…

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Q: 00 5 converges or diverges. If it converges, find its sum. 3m Determine whether the series > m= 2…

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Q: Question 7 The outer diameter of a spherical tank measures 6 feet. If the tank is made with a…

A: This question is related to volume of spheres, we will solve it using given information.

Q: The area of the finite region enclosed by the curves y = 3x and y 27 - a is given by the definite…

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Q: II. Find the Inverse Laplace of the following 2s-9 d. s² +2 1 е. (s²+1)(s²+4s+8)

A: As we know the Laplace transform identity; 1). L-11s2+a2=1asinat 2). L-1ss2+a2=cosat 3).…