25 2) V1x-91

Q: f(x)=/1+2sin x j. f(x)=e" +4* +sinh(10x)

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Q: Differentiate f (x) = 71n(x²-6x+3) A. (2x – 6) 7ln(x²-6x+3) f' (x) = x2 – 6x + 3 - В. In(7) (2x – 6)…

A: Given query is to find the derivative of the expression.

Q: 4x 9. sech(2x) dx e

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Q: -9 2. They" for y V3x-5

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Q: Find the area of the shaded region. x = -y 2 x = 2 - -2 A B 10 3 2.

A: Given query is to find the area of the shaded region.

Q: Write the first four terms of {an}. n + 1 10) an 3n - 1

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Q: Find an explicit formula for an. 15) 0, -1, 0, 1, 0, -1, 0, 1, . . .

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Q: Find V × (V × F) if F(x, y, z) = 5xyj+ 10xyz k. V × (V × F)

A: As we know that; If F→=F1i+F2j+F3k then ∇×F=ijk∂∂x∂∂y∂∂zF1F2F3 Given: Fx,y,z=5xy j+10xyz k

Q: Solve y’’ – y’ + y = 2sin(3x)

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Q: Determine whether the sequence converges or diverges, and, if it converges, find lim an. n-00 3 - In…

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Q: 3. If f(x) = [ 8+f dt ,find f'(1). .

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Q: 2. Find the desivative ofy= Binx

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Q: 2. Evaluate the following definite integral. You can assume the function is defined b the limits of…

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Q: Solve the triangle. (Do not round until the final answer. Round angles to the nearest degree and…

A: sine and cosine rule

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

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Q: Evaluate the definite integral. Use a graphing utility to verify yourr result. (sin(x) – 3) dx Step…

A: To evaluate the given difinite integral. By using a graphing utility to verify your result.∫0πsinx-3…

Q: Evaluate the trigonometric functions at the special angles. Match the function with its value. 1.…

A: To Find : Values of the given functions.

Q: 2. Calculate the area enclosed by the graph of y = x + 2x? - 5x - 6 = (x + 1)(x – 2)(x + 3)

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Q: The force F (in newtons) of a hydraulic cylinder in a press is proportional to the square of sec x…

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim t-0 eSi + sin(2t). -) +…

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Q: Find the area of the shaded region. x = 2- y2 -2 2 11 A 10 - 3. 8. D. 3. 2.

A: The area of the Shaded Region: the shaded zone's area is computed by subtracting the area of a…

Q: 1. Find the area of the region bounded by the given curves. Show the computed areas of sections…

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: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Here, the given vectors are: P(0,0,0) & Q(4,5,4)

Q: Find the direction angle of v for the following Vel v = - 6i- 3j What is the direction angle of v?

A: On solving this we will get

Q: csch 3x – 5 [3х — 10. dx V3x – 5

A: 10) To evaluate: I=∫csch43x-53x-5dx Substitute 3x-5=u⇒123x-5(3) dx=du⇒13x-5dx=2du3 ⇒I=∫csch4u2du3…

Q: dy -1

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Q: V100-1000 lim y-10

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Q: P1:

A: Solving

Q: 2. The area bound by the curve y = ezr, the y – axis and the line y = 4 is rotated about the line y…

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Q: P2: (e* sin x + x ln x) dx

A: The given integral is:∫exsinx+x lnxdxWe need to solve the above integral.

Q: Solve [æ – y cot ( ) dæ + x cot () dy = 0 ; y (5) = 1

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Q: dv 4.)Prove that f -Incosv + Insinv + C sinvcosv

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Q: Find the length of the curve z(t) = e“ cos(t), y(t) = e“ sin(t) for 0<t<7. %3D Give an exact answer,…

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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: system which is represented by the given equation below, is able to work effectively ven when the…

A: Given, f(x) = 7x ^ 3 - 0.31x ^ 2 + 8x - cos(x).

Q: 1. Find the area of the region bounded by the given curves. Show the computed areas of sections…

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Q: Compute the area bounded by the cardioid r(0) =1– sin(0) on 0, Express your answer as a decimal…

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Q: Evaluate the following Integrals: sin(4t) – 3 sin(2t)² dt 5 Vsech(4x) tan (4x) dx 1. 6. 7. sinh 3y…

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Q: g. f(x) =x' +Vx + h. f(x)=sec(3x)+ tan(5x³)

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Q: 1 If x= tand , then dr coso do . (1+x²) ½° A True B False

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Q: y = xx, x 4, and y = 0 Revolve the area of the shaded region about the line x = 4. Using circula…

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Q: 4. A live oak tree casts a shadow 58 feet long, Find the height of the tree if the angle of…

A: Here is the solution:

Q: 2 2 2 2 4' 16' 64' 256' 1024

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Q: C6. If FCX) =3x-4,43 li find F'(xland f"(x)

A: We need to find the first &amp; 2nd derivative of the given function

Q: Find dy for the given values of x and Ax. 5x - 4 y = -;x = 5, Ax= - 0.03 x+2 dy = (Round to three…

A: Given: y=5x-4x+2; x=5;△x=-0.03

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: f(x)= sin (x² +2x)

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Q: 7) For each set of parametric equations, eliminate the parameter and find a corresponding…

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Q: Find y ify=xIn(9x+1) 2.

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Q: Write the given decimal as an infinite series, then find the sum of the series, and finally, use the…

A: The sum of the infinite geometric series with first term a and common ratio r is given by…