Given the e dz nd y, find ar

Q: 12 12 f(x) dx = 16 and 9. If f(x) dx = 5, find the following. %3D f(x) dx

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) x3…

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Q: Q10. For the function f(x, y) = x³e³y_find the maximum value of its directional derivative at the…

A: Here, f(x,y)=x3e3y⇒∇f=∂f∂x,∂f∂y=3x2e3y,3x3e3y⇒∇f(1,0)=3(1)e0,3(1)e0=(3,3)

Q: 8) Find the linearization of f(x) = 6 + X+1 tan 4 dt at x = 0. 1.

A: On solving this we will get

Q: In Exercises 1-4, solve the given initial-value problem. (For Exercise 3, you may "complexify" the…

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Q: Consider the region bounded by x = 3y and x = y^3. A solid is formed by rotating the region about…

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Q: Find an equation of the plane. The plane that passes through the point (3, 4, 5) and contains the…

A: Given

Q: Scsc" 2 ede 4 CSC

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Q: Find the equation of the tangent line to the curve y 3 sec z 6 cos z at the point The !! equation of…

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Q: Find T(t) and N(t) at the given point. r(t) = (t2 – 3)i + tj; t = 3 T(3) N(3) =

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Q: 16. Interpretations of Integrals Determine the position function, s(t), of an object if the…

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Q: If a club consists of 13 ​members, how many different arrangements of​ president, vice-president,…

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Q: Find the slope of the tangent line to the graph of y = √x − 1 at the point (5,2).

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Q: Find the derivative of f(x) = log, (7x). (Use symbolic notation and fractions where needed.) df dx…

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Q: 2x3 dx 2x2-4x+3 3.

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Q: X – 1 limx → 1 V 4x – 2/x -

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Q: Question 1 Area bounded by the curves y=e", y=e", x=0 and x=In2 A 604/9 B 502/9 304/7 304/14

A: Ara of the above bounded curve is given by

Q: Find the derivative of f(x,y) = x +y in the direction of the unit tangent vector of the curve r(t) =…

A: The unit tangent vector T→t can be defined as the unit vector in the direction of the velocity…

Q: Calculate the derivative of y with respect to x when sin(x + y) = 6x + 4 cos(y). (Use symbolic…

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Q: Where does the line through (1, 0, 1) and (3, –3, 4) intersect the plane x + y + z = 6? (x, y, z) =…

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Q: Determine whether the series converges. If it does, find the sum: SUMMATION from n = 0 to infinity…

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Q: An individual needs a daily supplement of at least 312 units of vitamin C and 170 of vitamin E and…

A: Let, the amount of food I be x ounces.and, the amount of food II be y ounces. as the quantity of…

Q: (c) in the tank to a height of 1 m above its top. Give a definite integral that computes the total…

A: answer is in next step

Q: certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 59 - 2.2t…

A: Given query is to find the average temperature for the given time interval.

Q: 12. Find the flux of the field F(x, y, z) = 4xi + 4yj + 2k outward (away from z-axis) through the…

A: Flux of the given field is given by

Q: Jen would like to use the first week in May to visit one city, and the first week in June to visit…

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Q: Evaluate the indefinite integral. x2 dx V0.2x3 + 2.7 + C

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Q: The acceleration after t seconds of a hawk flying along a straight path is a(t) = 0.3 + 0.16t ft/s2.…

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Q: Evaluate the integral and interpret it as the area of a region. 6x + 7 - x dx 55, 55 - 32 9 9 Sketch…

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Q: Suppose we are given an integral of the form f f(g(x)) · g'(x) dx. We can transform this into…

A: The objective of the question is choose the correct option.

Q: For the following conditions, where "x= number of roses" and "y= number of daisies", determine…

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Q: Differentiate the function. g(u) = 7u + V 5u

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Q: Find the consumers' surplus at a price level of p= $160 for the price-demand equation below. p =…

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Q: 2 2 3/2\2 x' + -14 - %3D 2

A: Given query is to write the equation in standard form.

Q: Find the producers' surplus at a price level of p = $59 for the price-supply equation below. p= S(x)…

A:

Q: Calculate ri(t) · r2(t)] and [ri(t) × r2(t)] first by differentiating dt dt the product directly and…

A: Given that,  r1(t)=6t i+9t2 j+5t3 k,  r2(t)=t4k

Q: Convert the point from spherical coordinates to rectangular coordinates. (9, - =) (x, y, z) =

A:

Q: For what values of x in [0, 2T does the graph of f(x) = x + 2 sin x have a horizontal tangent? List…

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Q: Find the surface area revolve about x-axis at y = x³ from 0 < x< 2 98TT Answer: -sq. units 81

A: The curve y=19x3 from 0≤x≤2 revolved about x-axis.

Q: A piece of cardboard measuring 11 inches by 9 inches is formed into an open-top box by cutting…

A: A piece of cardboard measuring 11 inches by 9 inches.

Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = 4 cos(7t)i+4 sin(7t)j+ 3tk K(t)…

A: By using the formula kt=r't×r''tr't3 to find kt.rt=4 cos7t i+4 sin7t j+3t k

Q: 11. If f"(x)=-4sin 2.x, f(0)=0and f'(0) =2, find the value of f 4 %3D

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Q: ¤(x+4)~²dx

A: Here we have to find the given indefinite integrals.

Q: The acceleration function (in m/s²) and the initial velocity v(0) are given for a particle moving…

A:

Q: Activity 1.4.3. For each of the listed functions, determine a formula for the derivative function.…

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Q: - Determine whether L'Hospital's Rule applies to the limit below, then evaluate the limit 3r3 – 2x…

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Q: 5. S 2x' dx 6. S*-5x* dx x3

A:

Q: 350 The average cost of producing q computers per day is = 2- 422q + 1792, find the %3D dc Calculate…

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Q: ||r(t) x r"(t)|| ||r'(t)|³ Use the formula k(t) to find k(t). 13 r(t) = 4 cos(7t)i+4 sin(7t)j+ 3tk…

A: A detailed solution is given below

Q: dy 5. Solve the differential equation = 7xy3 if y = 0.5 when x = 2. dx

A: Given query is to find the solution of the differential equation.