Find the force on one side of a plate bounded by x = y² and x = 2 - y² which is submerged vertically in a liquid and the liquid is just covering the plate.

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A: We need to find critical numbers and classify them.

Q: 7 dx x4 - 16

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A: Here we have to find the limit of the function.

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Q: Find the derivative of the following functions by using the limit definition of the derivative.…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 1. - eu du (6 - e4)²

A: topic- indefinite integral

Q: The function f(x) = X = (6x 3) e5 has one critical number. Find it.

A: Given function ,   f(x)=(6x-3)e5x

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A: If value of y increases as x increases then function is increasing in that interval. If value of y…

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A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: Q1/B) Find the length of the cardioid curve: r = 1+ cose

A: A detailed solution is given below.

Q: Svi-x2 1-x2 dx

A: We will solve the problem

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A: Given query is to find the derivative of the expression.

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Q: Consider the function f(x) = x¹ − 50x² +11, x¹50x² This function has an absolute minimum value equal…

A: We need to find absolute max. and min. value.

Q: 7. 1 x lnx dx 8. f(x + 1)(2x - 1) dx

A: 7.∫1x lnxdx = ∫1 lnx. 1xdxLet, lnx= y ⇒1xdx = dySubstitute the corresponding values in the…

Q: Which statement is TRUE about trigonometric functions? O a. The derivative of sin x, cos x and tan x…

A: The answer with explanation is given below:

Q: t'dt √4+1² 19 dt

A: We have to evaluate ∫02t34+t2dt.

Q: Consider the solutions Y(t) of with a, b, d constants and a, b>0. Calculate lim y(t). t-x Hint:…

A: This question can be solved using the concept of linear differential equation and limits.

Q: [Select] 3x²+3 ³+3x-4 3x² +3 In{³+3-4} 1 ³+30-4 1 In{³+3x-4} 32-4) A. f'(2) 6.51 B. f'(2) = 1.5 C.…

A: Given function is  f(x) = ln(x3 +3x-4)  20) find derivative of f i.e. f'  22) find f'(2)

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Q: Find the maximum and minimum values of the function ㅠ g(0) = 60 - 7 sin(0) on the interval 0,…

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Q: If f'(x) > 0 at x = c, f(x) at x = c is

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Q: 150. Determine the real number a such that vectors a = -3i+2j and b = 2i+aj are orthogonal.

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Q: sin 3x cos 5x dx

A: ∫0π/8sin3xcos5xdx here we use formula  sinacosb = (1/2)[sin(a+b) +sin(a-b)]

Q: Solve the equation to find the value of a,b,c and d. Eqn 1: 6 = 6 b + d Eqn 2: 6 + 4 = 3b + c +…

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Q: Q3.If f(x,y)=sin(x-3y) + sin(x1 find: af 2x and af dy

A: We can find partial derivative with respect to 'x' and 'y' .

Q: Suppose that an accelerating car goes from 0 mph to 58.6 mph in five seconds. Its velocity is given…

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Q: 7 dx x4 - 16

A: Given: I=∫7x4-16dx   As we know the common integral. ∫1ax+bdx=1alnax+b+C And ∫11+x2dx=tan-1x+C

Q: dx 2√√x + √x

A: Solution of given question is written in below steps.

Q: dx (16+x)³3/²

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Q: In(3x) EXAMPLE 3 Calculate lim x → 00 SOLUTION Since In (3x)→ ∞o and In (3x) 1/x lim x → 00 = lim…

A: Topic = Limits

Q: 12 [ sin* ‡nxdx

A: We can find the answer as below

Q: A farmer finds that if she plants 65 trees per acre, each tree will yield 65 bushels of fruit. She…

A: A farmer finds that if she plants 65 trees per acre, each tree will yield 65 bushels of fruit.For…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) [ (In(x))²6 dx X

A: topic- indefinite integral

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A: Given:   Point : ( -1 , 2 , 5 ) Vectors : ( 2 , -1 , 3 ) and ( -3 , 1 , 5 )

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Q: A Farmer Wants To Enclose A Rectangular Area Along A Highway. The Fencing Along The Highway Will Be…

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Q: 150. Determine the real number a such that vectors a = -3i+2j and b = 2i+aj are orthogonal.

A: Given:a=-3i+2jb=2i+aj

Q: Differentiate the following functions using Chain Rule: 1. y = (4x + 3)² 2. y = √5x-2 3. y = (6x-4)²…

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Q: Given cost and price (demand) functions C(q) = 110q+40,700 and p(q) = 2q +870, what is the marginal…

A: Here we have to find the marginal revenue.

Q: For items 22-23: The equation of a curve is y = 5tanx. 22. What is the slope of the tangent line…

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Q: What is the second derivative of the function y = -6 sin x cos x where x is? Round your answer to…

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Q: If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air…

A: On solving this we will get

Q: 2. Use differentiation to find a power series representation for f(x) = 1 (1 + x)² °

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Q: 1. Find given x = 0 - sin 0 dy dx' y = 1- cos 0 1. Find dy given x = et-cos t y = et - sint 3. Find…

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Q: F. Change the Cartesian integral to polar coordinate dy dx 171-1 حول من كان الى بولير ار

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Q: Find the volume V of the solid E enclosed by z=9-y², 2-36-x, x = 0, and 2 = 0. (Give an exact…

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