Consider the circle in the ay-plane given by the parametrization x = 2 cos t, y = 1+2 sin t, 0

Q: 5. For which values of a and b the following function is continuous at x=-2 3x + a x -2

A: A function f(x) is said to be continuous at a point x=a iff limx→a-f(x)=limx→af(x)=limx→a+f(x)…

Q: X = -y A y 2Fx = 2- y² -2

A: Recall: Formula Area=∫abf(y)-g(y)dy  We have,  f(y)=2-y2, g(y)=-y

Q: cos(xy) + secy = 5

A: To find out the second derivative y".

Q: Perform the following operations and express the results in rectangular form: a. (8.21+j4.31) –…

A: Rectangular form

Q: Find curl(5z i+ 6x j+9y k). curl(5z i+ 6x j+ 9y k) = ( i )i+(i j+( i )k

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Q: The polar equation of the curve is expressed as r = 2sine + 2cose. area bounded by the curve.

A: To find the area.

Q: 3. Which of the following integrals requires integration by parts? A. S csc°0 de B. S cot*0 csc*0 do…

A:

Q: y y =x - 4 y =/2x + 8 4 6 10 x -2- -6+

A: Area bounded by the curves :   If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on…

Q: VI. Use Lagrange Multipliers to solve the following: Maximize f(r, y, ) = 4x + 2y +z subject to z +…

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Q: The integral of the given function 7 cos xdx is equal to а. 1 b. 2 с. -1 d. 3.1416 e. None of the…

A:

Q: P1:

A: Solving

Q: Find the volume by revolving the region of the curve xy = 6 from x = 2 to x = 4 about the x-axis.

A: Given xy=6        x=2 to x=4To find volume:

Q: a) Find the general solution to the differential equation f"(x) = e8x + 3x – 1 1.

A:

Q: 12. Which of the following is equal to dx upon decomposition? х3 — x2 -2х 1. 6 A. C. 2+ х - 2 dx x…

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: Explanation of the answer is as follows

Q: x-1 y = log x+1

A: Topic:- derivatives

Q: re' dy + +1 dr =0 O (y – 1) e + + In z = C 2. O-(y+1) e + Ine =C 2 O (1- y) e + 1. O 2y - e + +In=C

A: To solve given differential equation

Q: sin x cos x -dx (2 sin x – 1)(sin x + 1)

A: To solve: ∫sin⁡xcos⁡x(2sin⁡x−1)(sin⁡x+1)dx Let I = ∫sin⁡xcos⁡x(2sin⁡x−1)(sin⁡x+1)dx Substitute sinx…

Q: 1. Find the most general antiderivative of the function 12 f(x) = ( 2r + sin(4- r) + 7e

A:

Q: P3: | tan3 3x sec 3x dx

A: To evaluate: I=∫tan33x sec63x dx Substitute 3x=u⇒3dx=du⇒dx=du3 then: I=∫tan3u sec6u du3=13∫sec5u…

Q: dy - 3y= 5e* with initial condition K0) -5? dx Which of the following is a solution of the…

A:

Q: Find the length of the curve 7 (t) = (cos(3t), sin(3t), 2t) for – 8<t< 7 - Give your answer to two…

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Q: 8. (y- 2x)dx - x(1- xy)dy 0 Ans.

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Q: EQUATIONS DEPENDENT VARIABLE 5y (y/) = v sin e [Sclect ] - yy" + 2x tan a [ Select ] 3. [ Sclect] 4e…

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Q: y= Arccos(e2x)

A:

Q: 3x+1 5) lim x+ 2x +5 2+Vx lim ²-3x 6) 7) lim 2-Vx

A: Limits

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: 23. Find two numbers whose sum is 10 and the sum of their squares is a minimum.

A: Let the two numbers be  x and yx+y=10⇒y=10-xx2+y2=SS=x2+10-x2   =x2+x2-20x+100   =2x2-20x+100

Q: Suppose the table below gives the velocity of a moving object at any time t. Note that 7 IS measured…

A: We have to find the distance and graph of v(t).

Q: Find the general solution of the differential equation dx = xin (xy)

A:

Q: Q2. An object is kept at a distance of 20 cm from a concave mirror. A real mage is formed at 20 cm…

A: Topic:- algebra

Q: A cube 3 inches on an edge is given a protective coating 0.1 inch thick. About how much coating…

A: solution:-edge of cube=3 inchescoating=0.1total edge length of cube with coating=3+20.1=3.2…

Q: 9 5+ 8 g(x) 7- 4- h(x) 3- 5- 4- 2- 2- 1 1 2 3 X-values 3 X-values 1 g(x) , then h(x) If f(x) f'(3) =…

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Q: y = (e3*+4 +2)/(e²*3x +1)

A:

Q: 2x3 = (3xy + 1)2 Implicit Derivative with Solution (step by step using chain rule and product rule)…

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Q: 14. Given f'(x)= 5e* – 4 and f(0) = 2; find f(x).

A: We need to find f(x).

Q: dx The integral of the given function ſ is equal to (x²–2x+4)ž а. 1/4 b. 1/5 с. 1/6 d. 1/3 e. None…

A: A detailed solution is given below

Q: 2+ and g(x) = Figure out the domain of (fog)(x) in which f(x) = 4-x2

A: Given f(x)=2+x4-x2g(x)=1xHere…

Q: Find the Area bounded by the given curves. y = 2x + 1 ,  y = 7 - x ,  x = 8

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Q: Find the derivative of the following:

A: The given functions are:a. fx=3x+tan2xb. y=cos32x.We need to find the derivative of the above…

Q: Determine whether F(x, y) = 2x²yi+ 8xy j is a conservative vector field. If so, find a potential…

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Q: EXERCISES Solve the following differential cquations 1. =-sec(xy) Ans. sin x = +C dx 2x2 x +y Ans.…

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

Q: Type the correct answer In each box. -5 5 10 -20 0 a = b: and d%=

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Q: Find the area of the region bounded by the given curves. Show the computed areas of sections using a…

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Q: An isotope of the element erbium has a half-life of approximately 13 hours. Initially there are 24…

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Q: Give the value(s) of x at whichf has either a local minimum or a local maximum. Give the interval(s)…

A:

Q: Use the graph of the parabola to fill in the table. (a) Does the parabola open upward or downwa O…

A: a.   Parabola opens downward   b. Coordinate of vertax. Is (-2,-3)

Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few…

A:

Q: 1/5 2n'5 3) Use the Limit Comparison Test to determine whether the series V5n + 7n+7 n=1 is…

A: Given problem:-

Q: provide a step by step solution to the following bernoulli equation (y⁴ - 2xy)dx + 3x²dy = 0 ; when…

A: Let's find.