An equation of the plane passing through A(2,1, –1), B(0,–2,0), and С (1,-1,2) is: 7х — 5у — z %3 10 2x + y – z = 0 O This option O This option x - y + 2z = 1 x +y + 2z = 1 %3D

Q: To evaluate the integral 4+2a dr, we use Select one: O Substitution with a = 2 sin 0, where Substitu...

A: Given :∫4+x2dx

Q: Consider the function f(x) (-00, A, A, B), (B, C, and C, ) where A, and C are the critical numbers a...

A: Topic = Functions

Q: Find all critical points of the function f(x) = x-15 – x-16. (Use symbolic notation and fractions wh...

A:

Q: Given revenue and cost functions R(q)=80q−0.2q2 and C(q)=15q+500​, find the quantity that maximizes ...

A: This question can be solved using the concept of maxima and minima.

Q: 2nd deivative vong impliat dipperentiation x'y +y*x = X. -2

A: We can find the 2nd derivative of the given expression as below

Q: ( (cos(2r) – sin(2x)cos(2x)) -dx =. For +C. What is F (x)? cos(x) – sin(x)

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Q: By u = 1+r substitution, the definite integral z(1+ 2)"dr z is equal to Select one: O(1-u)u" du o S ...

A: Topic = Integration

Q: Find Vlak| for the series. k k k + 12 k=0 (Express numbers in exact form. Use symbolic notation and ...

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Q: Find dy/dx of the following functions. A. y = x⁵tan5x B. y = esec2x

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Q: II. Find the third derivative of the following: 2x-7 1. y = 2x+11

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Q: In (r? – 3) + e?-² at the 1. Find an equation of the tangent line to the graph of y = point (2, 1).

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Q: 5. y = XArctanx - In Vi+x

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Q: S(3x* – 5xP +x=³)dx.

A: Given query is to find the integral.

Q: Given cost and price​ (demand) functions C(q)=120q+43,000 and p(q)=−1.9q+850​, how many items must b...

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Q: If a rock is dropped from a height of 249 ft, its poistion t seconds after it is dropped until it hi...

A:

Q: A. Use the tabular method to evaluate the following limits. Set three values of x from each side. Ro...

A:

Q: Consider the points A(3, –3,5), B(5, –5, 2), C'(-1,–4, 2), and D(4, 1, –8). (a) Find the volume of t...

A:

Q: y- (6+5t-ビア 3.

A: We can find the derivative using chain rule as below

Q: Question 6 Evaluate the integral J sinh? COSA(2X) +C cost(2x) A sint(2x) B +C sinh“(2x) +C 8 cost4(2...

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Q: Given cost function C(q)=q3−125q2+2600q​, what quantity minimizes average​ cost?   It would be enter...

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Q: Find the area bounded by the given curves and lines. 1 (2-2)3 x = -2 x = 0

A: This question is based on application of integration.

Q: 1. y = x - x'cosx + 2xsinx + 2cosx 2sim x-1 2. y= cosx+2 3. tan(xy) + xy = 0 4. y= x 5. y = xArctanx...

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Q: dx = In[F(x)]+C.What is F(/3) if C = 0? For (x+x³) (x Tan-lx+1)

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Q: Using calculus, find the volume of the solid defined by 1<r< 3,0 <osT/2 and 0 < O ST.

A: The objective of the question is determine the volume of the solid at given region.

Q: Consider the function f (x,y) = x³ – 3xy + y³. Find all critical points of f and determine whether t...

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Q: 3 8. f (t) = (10t)z %3D 9. f(t) = tg'(t)

A: Given  f(t)=10t32 To find Laplace transform: 

Q: 5] compute: 7A -5B where: 2+3i itqi -si A = 3+7i -4 ?b-8 7 3ti 2+si ?5-8 5-2i -4-3i 8ミ チ+

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Q: I Find the second derivatively") of the following functions and simplity the final results. 1. y=x-x...

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Q: dx - = In[F(x)]+C• What is f(/3) if C = 0? For (x+x³) (x Tan-!x+1) 3 6. V3 +

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Q: cos2x – sin2.x cos2x - dx = -F(x)+C. What is F(x)? 3 For cosx – sinx 1 (A (sinx – cosx osx) - B sinx...

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Q: J, sin a sin? cos" ,dx COS 2 2 2.

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Q: 5. The management of Porter Airlines finds that its monthly marginal revenue can be approximated by ...

A: Find your answer below 

Q: 1 n > 3. Let an n Vln n Use the Integral Test to determine if the series > an converges or diverges....

A:

Q: Determine the values of a, b, and c such that the cubic function f(x)=ax^3+ bx^2+ cx satisfies all o...

A: Given problem:- Determine the values of a, b, and c such that the cubic function f(x)=ax3 + bx2 + cx...

Q: (1x) +3 . Is-3 Check the continuity of f(x) ={-2x , -3 <x< 3 12 3 (6x + 2 ,

A: Here we have to check the continuity of the given function f(x).

Q: u = 2i + 3j + k v = i+j+ 4k w = i+ 3j + 8k

A:

Q: Carbon decays exponentially. How many grams of the carbon will be left in 139 years, if 123 grams we...

A: Initial amount P0=123 grams time t=96 years Amount left after 96 years =P=66 grams Exponential decay...

Q: C b 630 A 53

A: Topic = Triangle

Q: Question 3 The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies ...

A: ∫-b-a1+xfxxdx = ∫-b-a1xdx +  ∫-b-afxdx = lnx]-b-a + ∫-b-afxdx Given ∫fxdx = Fx and Fx is odd functio...

Q: c). Classify the equation below with all the possible characteristics and properties of a differenti...

A: General form of Linear differential equation of first order and first degree is given by dydx+yP(x)=...

Q: 3. The diagram shows a cuboid that is formed by bending a long wire of length 336 cm?. 3x (c) Find t...

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Q: Exercise 1 Determine the relative extrema of f. (b) f(x, y) = 4xy² – 2r*y – x -

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Q: dx =In[F(x)]+C•What is F(/3) if C= 0? nk+1) For (x+x³) (x Tan

A:

Q: 3. A function is defined by the equation y = V3x + 4, where does the slope of the tangent line equal...

A: Given,           A function is defined by the equation y=3x+4 and the slope of the tangent line     ...

Q: he given series converges or diverges. use the following as proof: rison Test, Integral Test, Series...

A:

Q: 5. Water is pumped out of a horizontal cylinder through an opening at the top. Find the work (in jou...

A:

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the eract answers using the provide...

A: (a) The vector v→=9i→-12j→ as v=(9,-12). Let a vector in opposite direction of v=(9,-12) be u→. Fin...

Q: x2 - 3x - 10 s 0 ² - 10 s 0 O [5, 0) (-0∞, -2] or [5, ∞) O(-00, -2] O(-2, 5]

A: Topic = Inequality Correct Answer [-2,5]

Q: Given Cost and Revenue functions C(q)=q3−8q2+52q+5000 and R(q)=−3q2+2500q​, what quantity minimizes ...

A: Minimize marginal cost

Q: Q4) Find the Asymptotes of the following functions: x³ – 4x² - 1) y x² – 2 x² – 4 2) f(x) : %3D x² –...

A: Solution is given below