1. A vector is: a. a quantity whose magnitude can be completely specified by a number b. a quantity that represents magnitude only c. a mathematical quantity with magnitude and direction d. a quantity that represents a direction only

Q: x* dy

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Q: Find the following definite integrals. sin a dr

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Q: 2tan 'x -x (-) 2x – sin 'x 02. lim, -1

A: Given limx→02tan-1x-x2x-sin-1xTo evaluate the limit:

Q: (sec2 x + csc2 x)cos2 x dx

A: Given: I=∫sec2x+csc2xcos2xdx   Use the trigonometric identity; 1). sinx=1cscx 2). cosx=1secx And…

Q: 2 x= - 5, x=2, y = 5x, y =x -6

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Q: 1. Using proof by contradiction, prove Let n be an integer. If n' is even, then n is even.

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Q: 3 * 12(In x)³ dx

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Q: X+0.4Inx 04. lim,+ X+ 3lnx

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Q: 28. y' ry + 1; (ry+ 1)dr- dy 0 29. dr- dy 0 %3D

A: Differential equations

Q: se implicit differentiation to find hp without first solving for y. dæ æª + 3æ°y + y² = 15 ,10, dy…

A: Given query is to find the derivative and equation of tangent.

Q: Find the centroid of the solid generated by revolving about the indicated axis the area bounded by…

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Q: 3- Jッ 2X e dy + 2 (y ē -x) dx =0. dy よx 4- Sinx + cosx y = tan x

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Q: y = 5x2 – 3x – 4 | | Finding the derivative of y: y = 5x? – 3x – 4 y' = 10x – 3 Finding the…

A: A detailed solution is given below.

Q: 2. Define f, g: R → Ras if x 3 %3D and g(x) = 8x – 1. Flnd f •g and gof.

A: (fog) (x) = f(g(x))                = f(8x-1) =(8x-1)^2  if x<-1                                =…

Q: ind a parametric equation for the line that is perpendicular to the graph of the equation 3x + 4y +z…

A: We find  a parametric equations for the line that is perpendicular to the graph of the equations 3x2…

Q: %3D Find the derivative of y = Vsinx COS I 2sin z 1. -sin z H S00 5.

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Q: Test whether the differential equations are exact and solve those that are. I- y = %3D 2yt+1 -2xy…

A: Given

Q: 7. A(2,–3) and B(5, 1) are two points in R². Determine the following: a) AB b) |AB| c) a unit vector…

A: We can solve this as follows:

Q: 3.2 Inductive Reasoning Use inductive reasoning to make a conjecture. Note: The numbers 1, 2, 3, 4,…

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Q: y = , x = 1, x = 4, and y = 0 is revolved about the y – axis. (Answer: 247 c. u.

A: Recall: Shell Method  V=2π∫abr(y)h(y)dy We have, r(y)=y, h(y)=4y, a=1, b=4

Q: The value of the triple integral 6zdV where E is the upper half E of the sphere of x² + y? + z? = 1…

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Q: 37. A 10-m ladder rests against the wall of a house. The foor of the ladder on the ground is 1.3 m…

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Q: 1. Which of the following relations is FALSE. A) (ab)" = a"b" B) C) (a")" = a"* D)

A: Note: As per company policy we are supposed to solve only 1 question. So, kindly repost others.…

Q: (h – 2) - 4 (i) lim 2h

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Q: in terms of x and y for the points (x, y) A5. (a) Use implicit differentiation to find that lie on…

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Q: . lim, 1 -2 Inx x-1

A: To evaluate the given limit

Q: 3x2+2 dx 0 2x2+4x+3 In |2| 2 In |3| 2 Option 1 Option 2 In |3| 2 In |2| 3 Option 3 Option 4

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Q: 14 V1+ 7x dx

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Q: 8 Given a function: f(x) (х-7)(х-1) Write down the definition that lim f(x) = L = 1| 8 oProve that…

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Q: Evaluate the following indefinite integral. dx dx = (Type an exact answer.)

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Q: 2. xy -(xy? cot Cans ☆ +y?)

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Q: e If F(x) = | e dt, find F(1) and F'(x). ez

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Q: Activity 1. Determine the antiderivatives of the following functions. 1. f(1) = (1+1)100 2. f(x) =…

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Q: (x-3)² 1) 6-4)² =D1 16 196 (x+ 1)² ¸ (y – 8)² 3) 9. =D1 %3D 81

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Q: An airplane is on a heading of 235° at 600 km/h and a l10 km/h wind is blowing from due west.…

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Q: Find the value of c so that f(x) is continuous at x = 3? x2 f(x) = x 3

A: Given query is to find the value of c.

Q: dy without first solving for y. dx Use implicit differentiation to find - 28x4 + 10x2y + y* = 8 dy…

A: The given function,    -28x4+10x28y+y4=8

Q: Evaluate the integral: *Input answer as decimal round-off to 2 decimal places.

A: Given problem:-

Q: 4 dx 4-x2 Evaluate

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Q: 8. Evaluate * y" – 3y' + 2y = e3t ; y(0) = y'(0) = 0 e2t -e3t + 2 et 23t -e2t + 2et 2 O A. e3t -e2t…

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Q: Calculate the area of the puddle when 10 liters of water is spilled on a flat floor for cases of 0p…

A: Water molecule have an enormous amount of inter-molecular forces.  10 liters of water would spread…

Q: dy =-2x tan y, 1- y(0) = 1/2. dx 2- 2 ydx CSOS 3- e*dx-ydy 0, y(0) = 1

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Q: Evaluate the integral: S2 (2x + 6) dx Input answer as decimal. Round off to 2 decimal places.

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Q: To find two real numbers whose sum is 23 and whose product is maximum, we should find the maximum…

A: We have to choose correct option

Q: Find the derivative of f(x) = (2x^2-x-1)(sqrt of x) %3D

A: A detailed solution is given below.

Q: Rewrite the expansions in terms of exponential and simplify the results as much as you can. 1. 2…

A: We use the formula of coshx and sinhx to simplify the given expression.

Q: Suppose that f(x, y) = x' + y – 2xy Then the minimum is

A: Solution is given below:

Q: Use the tabular method to evaluate the integral |* + 2x – 1) cos(42)dx

A: Explanation of the answer is as follows

Q: If = 27- 67 + 2k and y = i+3 - k, determine + 25.

A: Topic = Vector

Q: 4 find f'(3). x2 If f(x) =

A: