Find a unit vector u in the direction of v = (2,-1,5) Ou-( 30 /30 1. u = 30 30 O None of these (4,1, 25) Ou=

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A: We will find the relative extrema and the value of f"(2) as following. The function given f(x)=x^2…

Q: After substitution is performed, what is equivalent to /, x sin x² dx , 3 sin u du 8 sin u Li du 3 L…

A: solution is given below

Q: 1. Solve the given the equation using the integrating factors found by inspection. ydx + (x + x³…

A: Given that ydx+x+x3y2dy=0Solution :ydx+x1+x2y2dy=0this diffrancial equation in the…

Q: AVERAGE VALUE OF A FUNCTION QUESTIONS A. 3x2+4x-7, [-2, 5]

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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Q: Idx/(1-2x) = 1/2 In]1 -2x + C Select one: O True O False

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A: Find your answer below

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Q: Evaluate lim f(x+h)-f(x) h-0 where f(x) = 2 – 3x². h None of these -X 6x O -6x O 3x

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Q: true or false 1. ∫dx/(1 - 2x) = 1/2 ln|1 - 2x| + C 2. ∫ (1 - 4x4 + x3)/x3 dx = 1/(2x2) + 2x2 - x…

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Q: The integral of the given function ſ cos 3ydy is a. sin 3y +sin³3y + . sin³3y – sin³3y +sin53y + C…

A: Topic :- application of integration

Q: vo Variables 4)dr + (2r. (2. 4x)dı

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Q: 8 4 4 -7 (a) h(x) = 7X 1 -7 (b) g(x) = 7x (c) k(x) = - 7X %3D %3!

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Q: Find the iimit oT X SP approaches zero from the left. x -3.62330136 t-0.827974189 4- 2 10 12 does…

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Q: 4. (Straightforward) Determine if each of these differential equations is exact, and if so, solve…

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Q: Substitution Method dy xy = 0 (7) (x² – y²) (8) 2xy = x² + 2y² - - dx dx (9) (1 1 3r sin v)dr r2 cos…

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Q: Suppose the position of a particie is given by parametrc equations x(e) = -3 and y(t) = 2?. (a) Find…

A: The given data is: xt=t3-3yt=2t2  (a) To find the particle's position (x,y) at t=3

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A: Please see the answer below.

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Q: Suppose f'(x) = sin(2x²). d ; f(7æ) =| dr d de f(32®) = [

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Q: Vx- 2 Evaluate lim x-8 x2-7x-8 O 2/7 None of these O 1/9 O 1/12 O O o O

A: The given limit,     limx→8x3-2x2-7x-8

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Q: |(1 - 4x4 + x)/x dx = 1/(2x2) + 2x² - x + C Select one: O True O False J(4csc?x -3sec2x) dx = -4cotx…

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Q: 6.(Somewhat tricky) Use an appropriate substitution to solve: (a) dy y + x dx (b) (y³ + y?x) dx – x³…

A: To solve the following differential equation

Q: Use the following information to answer the next three questions. A model of a house was built using…

A: 2.5cm corresponds to 1m.

Q: xdx Evaluate (x²-2)5

A: Given query is to evaluate the integral.

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Q: af Given f(x, y) = In(6x² + 8y²) then %3D

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Q: Answer the following True or False. 4 + C In 4 O True O False

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Q: Sdx/(1-2x) = 1/2 In[1-2x + C Select one: O True O False S(8x + 2x) dx = 2x4 +x2 Select one: O True O…

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A: Given query is to find the maximum height.

Q: Find the maximum value of the function f(x) = x³ -9x2 + 15x - 5. Answer: Find the value of x for…

A: In order to find the critical values we need to differentiate f(x) with respect x and then equate it…

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Q: Answer the following True or False, sin dt 圭 dt 0. 1 t? t cos O True O False

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Q: 4. V40-4v-v² dv – 4v

A: This question can be solved by using the concept of some special integrals.

Q: Let the region R be the area enclosed the function f(x) = x², the horizontal line 6, and the y-axis.…

A: Explained below

Q: 13n Illustrate and find the smallest positive coterminal angle of 3.

A: We have to find smallest positive coterminal angle of -13π/3. And we have to illustrate that angle…

Q: An angle's initial ray points in the 3-o'clock direction and its terminal ray rotates CCW. Let θ…

A: I am attaching image so that you understand each and every step.

Q: *5. Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the…

A: We need to use the approximated formula of area of the respective methods.

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Q: Find the dimensions of a rectangle with area 216 m² whose perimeter is as small as possible. (If…

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Q: EXACT VALUE OF C IN INTERVALS QUESTIONS (such that f(c) = fave) A. 3x2+2x - 4, [-2, 4]  B. 5cos(x)…

A: As per our guidelines we are supposed to answer 3 sub-parts , kindly repost the remaining part as…

Q: Find an equation of the tangent line to the graph of f(x) = xe−x at its inflection point.

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