I.TRUE or FALSE: Read carefully the statements below. Choose A if the statement is ALWAYS TRUE, otherwise, choose B. Click on the letter corresponding to your response.( The derivative with respect to x of any constant multiple of the exponential function y = ex is equal to itself. If f(x) is any polynomial of degree 10, then the 9th derivative of f(x) is zero. 5. If f'(0) = 0, then f(0) 0.

Q: Consider the function y-2+3x² -x³ a) Find the intervals on which this Punction is increasing or…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the point (2,…

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Q: Find the volume of the parallelepiped determined by the vectors ā = (5, 4, – 1), b = (0, 1, 4), č =…

A: Given query is to find the volume of the parallelopiped.

Q: Find the area of the region bounded by the graphs of the given equations. Enter your answer in exact…

A: Given :

Q: 8 Evaluate for (3x² -7x+4

A: We have to use the concept of derivatives

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A: Here, the given function is: y=7cos(8x) Note that the period of the function is: 2π8=π4 Now, the…

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Q: If f(x) = 2 g(x) find g'(x) in terms of f'(x). O g'(x) = f(x)/2 O g'(x) = 2 f(x) O None of these O…

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Q: Find the first four nonzero terms in the Maclaurin series for f(x). f(x) = e 5x sin x ... Choose the…

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Q: Write the augmented matrix for the system of linear equations. 6x +y+ 3z =D 2 9x - 6y- z = 5 x-8y-6z…

A: Explained below

Q: Find curl (9z i+ 10xj+ 2y k). curl (9z i+ 10x j + 2y k) = ( i Di + ( i j+ ( i )k

A: We have to find the curl

Q: dy Solve the differential equation = -3 cos x-4x if y(7)=0. dx

A: To solve the given differential equation.

Q: II 2. 3. 2. 4. x² 1. X. 3. D3x 4. 1. Find the given derivative. 4-part 1 Homework: Homework Chap

A: Dx3x-12 + 4x32=Dx3x-12 + 4x-32                               =3Dxx-12+4Dxx-32…

Q: Evaluate F. dr. Jc F(x, y) = 7xi + 8yj C: r(t) = ti + v4 - tj, -2 st s 2

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Q: Evaluate the integral / (2x + 9y)dx + (6x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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Q: Let S1 be the hemisphere with Cartesian equation z = 6 – /36 – x² – y? and S2 be the upper nappe of…

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Q: 4. Evaluate lim (cos r)/**.

A: We know that limx→0f(x)g(x) is of the form 1∞ then limx→0f(x)g(x)=limx→0eg(x)f(x)-1

Q: Sx³e*²dx 3. X°e

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Q: (i) Using Laplace's equation, find v,and və for inviscid vortex flow.

A: answer is in next step

Q: valuate the indefinite integral. 7 dt (t + 1)?

A: Given query is to eveluate the integral.

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A: We have to use the concept of derivatives

Q: Compute f, for f(x,y)=xln(xy). %3D

A: We can find the answers as below.

Q: Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = ze'i + x cos(y)j + xz sin(y)k, S is the…

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Q: Describe the graph of the equation. r = (7 – 21) i + 10r j | O It is a line in 2-space through the…

A: The given equation is: r(x,y)=(7-2t)i+10tj⇒x=7-2t    y=0+10t

Q: D If the Taylor series expansion for f (x) is given by f(x) = Eo- (x- 2)*, then f(4) (2) = %3D

A:

Q: QUESTION 12 Eliminate the parameter to find a Cartesian equation of the curve. x-e'- 1, y - e Select…

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Q: Find the derivative of f(x) = (2 - 3x) (-5x + 4). O 2 О 22-30х О зох + 22 30x + O 15x + 8 None of…

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Q: 3. If dt , find g'(2). 5. g(x) =

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

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Q: a" + C,C E R. In a If a is any positive number except 1, then a" du True False

A: The given statement is True.The exception exist at a=1 because then in denominator we will have ln1…

Q: Find a plane through the points (4,-3,-4), (-6,2,8), (3,-8,8)

A:

Q: ntinuous function, f (x), has a domain of [-6, 6] -6 <x<-2 x=-2 -2 <x< 0 x=0 0 < x<6 does not exist…

A:

Q: 3. Suppose that the revenue in selling a tables is equal to 200.x -0.25a2 dollars, and producing a…

A: We know that profit=selling price-cost price

Q: 4. Find the equation of the tangent line and normal line that passes through the circle (x – 2)² +…

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Q: Find the area with respect to y of the region bounded by x = y² + 2 , x = 0 , y =– 1, and y = 2. |

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Q: ||r(1) × r"(t)|| Use the formula «(t) to find «(t). r(t) = 11 cos(t)i + 11 sin(t)j + 6tk K(t) =

A: We can solve as follows

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Q: (y – x) dx + 15x?y? dy

A: answer is in next step

Q: Find V · (V × F), if F(x, y, z) = 2e"*i+4xe"j – 4c*k. V · (V × F) =

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Q: Write the augmented matrix for the system of linear equations. 6x +y+6z = 8 3x- 7y-z = 6 x- 4y - 5z…

A:

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). 3 r(t) = 11 cos(4t)i+ 11 sin(4t)j+ tk K(t) =

A:

Q: Evaluate the line integral | -ydx + xdy along the curve C:y? 30x from (30, 30) to (0,0). NOTE: Enter…

A: We need to find integral.

Q: Draw a graph that does not pass through -8 and 8. Identify 3 points that is continuous at that…

A: Solve the following

Q: II P. Do Homework -Homework Chapter 4- part 1-Google Chrome…

A: Given query is to find the point where slope of tangent to the curve is zero.

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Q: Determine the gradient of f(r, y) = ez sin(5y) at (r, y) = (3, – 1). Round to 2 decimal places. V…

A: Given query is to find the gradient at indicated point.

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

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Q: ) = x/x² + 36 ned on the interval – 4 < x < 5. ) is concave down on the interval x = to x = ) is…

A:

Q: Given the function below f(x) = V-80x + 144 Find the equation of the tangent line to the graph of…

A: Given :