Si x³VI+x* dx? After substitution is performed, what is equivalent to 82 4 vũ du 82 Vũ du 82 Vu du 4 Vũ du 4

Q: If f (z, y) — е"у, then fr (1, In (3)) —??? (а) е (b) e³ (с) 1/3 (а) 3 (е) 3ln (3)

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Q: Verify that the function satisfies the three hypotheses of Rolle's theorem on the given interval.…

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Q: of

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Q: Integration by trgonometric substitution 1. S_dx (4x-x2) ³12

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Q: Evaluate this path limit: 4.ry3 lim (z, y)¬(0, 0) 2x² + y6 I=y% =???

A: To find: Limit of the function of two variable along the given path.

Q: æ = 4;y = t-1»Y t² – 1|

A: Use the following derivative formulas:ddxxn=nxn-1ddxfxgx=ddxfxgx-ddxgxfxgx2ddx ( f(g(x) ) = f'…

Q: Consider the following scenario: The rate of increase in the number of p who have committed drug…

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Q: 2. The solution to the equation below is x = 2 and x = 5. cos? æ – 7 + 10 = 0 O True O False

A: The given equation is:

Q: 8)Suppose the total cost of a certain product is C(x) = 0.001 x2+ 5x + 300. The product can be sold…

A: Find your answer below

Q: Directions: In implicit differentiation, we differentiate each side of an equation with t variables…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find an equation of the plane with the given characteristics. The plane contains the y-axis and…

A: Given that the plane contains the y-axis and makes an angle of pi/2 with the positive x-axis. Here…

Q: Find the first three nonzero terms of the Maclaurin series for the function and the values of x for…

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Q: Find the points on the curve r = 1– sin 0 - where the tangent line is horizontal or vertical.

A: To find out the points on the given curve, where the tangent line is horizontal or vertical.

Q: wes You are to construct an ofen rectangul 22 of material what dimensions will resultin

A: We are asked to find the dimension of the rectangular box.

Q: III. SOLVE THE FOLLOWING INDETERMINATE FORMS e* +e* – x? – 2 1) Lim sin? x - x? 12+ x? 2) Lim X 00 X

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Q: Let the cost function be C(x)= x2 / 8 + 4x + 200 and the unit is sold at price of p = 49 - x dollars…

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Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLIFIED FORM 2. Y= 2 Arccos (1-)+ v4x – x?

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Q: A colony of bacteria starts with 2000 individuals. The colony is exposed to a new penicillin-type…

A: Find your answer below

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Find the derivative using the definition 2х-3 y = 3x-2 What is the solution if the answer is: 2х-3…

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Q: The width of a rectangle is increasing at a rate of 5 cm/sec, while the length increases at 6…

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Q: Julia is a lifeguard and spots a drowning child 30 meters along the shore and 60 meters from the…

A: Answer of given question is in next step

Q: Learning Task 2: Expand each function (using the appropriate technique/ formula). Compute the…

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Q: Determine whether the planes are parallel, orthogonal, or neither. 9x - 3y + z = 4 x + 4y + 3z = 1 O…

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Q: (a) Differentiate f(x) = Vx+4 by using the first principle. (b) Differentiate the following…

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Q: Find a point P on the line and a vector v parallel to the line by inspection. Enter the vector i as…

A: Explanation of the answer is as follows

Q: dx J 2x+Vx 1.

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Q: Find the second derivative of g(x) = sinh(x) cosh(x)

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Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not…

A: After solving the problem, we get only one equation. But, there is three variables. So, we have to…

Q: (b) Given -3x + P for x7 Determine the value of p if f(x) is continuous at x=7. TEST DMI123

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Q: Given vectors a = (-1,-2),5= (-2,3), c= (3,-1),đ = (-3,2) find the dot product of 5 and d. -12 -1 12…

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Q: find y' (xy)x = e

A: Given problem:- find y'   (xy)x = e

Q: Find sets of parametric equations and symmetric equations of the lihe that passes througn the given…

A: Here we have to find the sets of parametric equations and symmetric equations of the line that…

Q: e* – 9dx = 2ve* – 9 – 6Arctan ( Ve 9) +

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Q: 2 2 X = 1+t2 y=r(1+t?)

A: To find second derivative of given function.

Q: Directions: In implicit differentiation, we differentiate each side of an equation with two…

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Q: Determine whether u and v are orthogonal, parallel, or neither. u = (cos(0), sin(0), 9) v = (sin(0),…

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Q: Just algebkaiçal fing the inverse function of f in formally VeRify that f(e10)) =x and

A: Here, to find the inverse of each function and then verify f-1(f(x))=f(f-1(x))=x

Q: y = In (*+1) °(x+1), (x+2)3

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Q: cot (3x) За co dx csc 3x + 1

A: To evaluate the given integral.∫cot33xcsc3x+1 dx

Q: Find minima, bmakima and Sndtle pointr for the funetionss fex,y)=4x 6xy+ 5y- 20 x +2by…

A: a) If df/dx=0 , d2f/dx2<0 at x=a then fx attains maxima and maxima  value is f(a) . b)   If…

Q: Sales of a Product The total number of units of a new product sold t months after its introduction…

A: see below the answer and explanation

Q: ) Find the y’’ (second derivative) of the following in its simplified form. Do not skip the steps…

A: This is a problem of differentiation of the function. Based on the general formula we will solve the…

Q: In each part, use a scalar triple product to determine whether the vectors lie in the same plane.…

A: a) u=2,-2,2, v=3,0,-2, w=5,-2,0u.v×w=2-2230-25-20u.v×w=2(10)+2(-4-6)u.v×w=20-20u.v×w=0Since ther…

Q: Find the length of the curve y = = cosh(x), 0 < x < 1. Arc length =

A: Arc length of a curve y=f(x) on [a,b] is given by, L=∫ab1+y'2dx ddxsinh(x)=cosh(x)…

Q: Learning Task 2: Expand each function (using the appropriate technique/ formula). Compute the…

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Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 300…

A: Given problem:- A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder…

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A: A line will lie in a plane if any two points on the line also lies in that plane. As we know between…

Q: 3. dy = (x - 3y)dx ans. 9y = 3x - 1 + ce 3

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Q: 3. Express the following integral as a one-dimensional integral in term of r, where E is the region…

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