EXERCISES 2: Find the derivative of the function at Po in the direction of A. 1. f(x, y) = 2xy – 3y², Po(5, 5), A = 4i + 3j -

Q: A particle moving in a planar force field has a position vector x that satisfies x' = Ax. The 2x2…

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Q: Use hyperbolic functions to parametrize the intersection of the surfaces x2 - y = 9 and z = 5xy.…

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Q: y = 2x' - x' +x+1 when x =1

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Q: Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify…

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Q: Show that Q(V3, V3) = Q(v3+ V3) %3D

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Q: f(x) 8 -7- -6- 5- -3- -7 -6 -5 -4 -2 -1 0 2 3 5 9. 7. 9 10 11 12 -1- 9, 2.

A: Here we need to answer some basic questions based on the graph.

Q: Given two functions h(t) and g(t), is h¯1g-1 (t) = (hg)-1(t).

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Q: * f(x) = x —х+ sin(x) — 1 Solve this question by the Bisection method on the topic of solution of

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Q: a) ū =(4,8,2) and v = (1,4,6) %3D

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

Q: Identify the open intervals on which the function is increasing or decreasing. g(x) = x2 – 4x – 12…

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Q: 7 p(x) = iven the expression Vy7 – 2 this mathematical expression stated correctly.

A: Given query is to find expression is correct or not.

Q: 4. A thermometer is removed from a room where the air temperature is 70°F and is taken outside,…

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Q: Consider the parallelepiped with adjacent edges u = 9i + 8j + k v = i+j+ 9k w = i+ 6j + 5k Find the…

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Q: 13. A town's population in 2000 was 36,000 people. In 2005 the population had risen to 54,750.…

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Q: Find dy/dx of the following function

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Q: The graph of f consists of line segments and a semicircle, as shown in the figure. Evaluate each…

A: To find the given integration using the given graph.

Q: Find the gradient of the function at the given point. In(x2 - Y) - 9, (3, 8) Vz(3, 8) =

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Q: %3D 3. For y = f(x) = 6x, x = 4, d and Ax 0.08 find a) Ay for the given x and Ax values, b) dy…

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Q: Let f(x) = x and compute the Riemann sum of f over the interval [8,9], using the following number of…

A: n=2 x 8 8.5 9 f(x) 512 614.125 729   Reimann sum using left-endpoints: ∑i=1n-1 f(xi)…

Q: 3. Use the fact that F = is a conservative vector field to evaluate SF. dr when C is the path r(t)…

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Q: For a certain bathtub, the hot water faucet can fill the tub in 12 minutes. The cold water faucet…

A: Efficiengy of hot water faucet (Eh)=work time taken by hot water faucet to fill the tub (Th)Since…

Q: Describe the given region in polar coordinates. R:OsrsOOs0s (Type exact answers, using x as needed.)

A: The given region represents areashaded between two circles:x2+y2=32x2+y2=42In polar coordinates;x=r…

Q: 1. f o" xy dy dx О а. 32/3 ОБ. 16/2 Ос. 32/4 O d. 18/4

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Q: 12. The terminal point P(x,y) determined by an angle t (a) cos (t) (b) tan (t)

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Q: 6. Solve the following equations for the unknown: i) 4 3n = 32 ii) log2(y +1) + log:(y– 1) = 3 iii)…

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Q: A bicycle's gear ratio is the number of times the freewheel turns for every one turn of the…

A: Let's find.

Q: Find the area of the region enclosed by the inner loop of the limaçon r = 11+ 22 cos 0. [Hint: r < 0…

A: To find the area of the region enclosed by the inner loop limacon. Given r=11+22cos (theta)

Q: 1 Imit |2 – x| x → 2

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Q: Liaed the Residuesof fucation coske)

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Q: Find the area of the shaded region. 160- (5,150) f(x) = x - 8x + 21x2, g(x) = 20x + 50 (-1,30) 10

A: Given,            fx=x4-8x3+21x2 , gx=20x+50           To find : Find the area of the shaded…

Q: Find an equation of the circle whose diameter has endpoints (5, 1) and (-1, -3). O=0

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Q: Given that the acceleration vector is a(t)= the initial velocity is v(0)=, and the initial position…

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Q: Find an angle 0 with 0° <0< 360° that has the same: Sine function value as 250° 0 = degrees Cosine…

A: Find your answer below

Q: 2. Find the value of xy dx + Vy2 + 1dy, where C is the path shown on the graph below. (Hint: Use…

A: We have to find the value of  ∫Cxy dx + y2+1 dy. Given the path C is

Q: Find the derivative. Simplify where possible. |(a) y = ln(coshx)

A: Find the derivatives

Q: Find the amount of an annuity with income function c(t), interest rate r, and term T. (Round your…

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Q: There is a power plant that charges 10 cents per kilowatt hour for electricity and produces 1,000…

A: Given query is to find marginal cost.

Q: The marginal cost function is the derivative of the cost function. If the cost function of producing…

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Q: Given the triangle below, find the angle 0 in radians. Round to four decimal places. 7 4 Provide…

A: Topic = Triangle

Q: x =r' +1, y=r -t = t° a) Find dy/dx Show all your work.

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Q: 2. A particle is moving with acceleration a(t) = x - 3 sin(x). Find the velocity and position…

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Q: Suppose the temperature in degrees Celsius over a 10-hour period is given by T(t) = - t + 6t + 36.…

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Q: 5. The initial value problem which describes the motion of a certain undamped harmonic oscillator is…

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Q: (-1)"-1 (In n)" 00 23. E n=2

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Q: Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.…

A: Formula used:logan=nlogalogab=log(a)-log(b)loga.b=log(a)+log(b)

Q: Solve the pic using integration by parts. Do not use other method. Show the complete solution and do…

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Q: finite difference du n. = 0 en 0 0; dx² - u(0, t) = u(2, t) = 0, 0 < t; %3D u(r, 0) = sin x, 0<x <…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 - 2xy + y2,…

A: This question is based on finding equation of tangent plane.

Q: dx (2x – 3)v5 – 12x + 4x² |

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Q: Three Vectors are given as shown. 40 60 In the figure above, the magnitude and direction of the…

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