Substitute the above values In the equatlon for (3/+ B) (31 + 8) = + 48 II II

Q: Use series to evaluate the limit. 4 3 sin(2x) – 2x + lim 4/3

A: Given problem:-

Q: Find the roots Lzerel of eah tunction and State tHhe multipicty of any veputed root - 니 2x

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Q: Find f'(2).

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Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: Find the sum of the series. s 7(-1)"72n + 2n + 1(2n + 1)! 00 Σ n = 0

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Q: Find an explicit formula for an. 1 1 4'9' 1 1 14) 1, 16' 25

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Q: 7 Determine the intgral

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Q: Find the first derivative with respect to the domain variable for the following functions. 4. f(x) =…

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Q: (a) Find the value of P(?, 4) and P(?, 6) using permutation formula, where ? is the last two digits…

A: Permutation: Permutation:  The permutation is a method of arranging objects in a specific order.…

Q: (d) lim Use the graph of the function f to decide whether the value of the given quantity exists. If…

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Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: Now, find the

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

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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: Change the Cartesian integral to polar coordinate | +y*)dx dy

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Q: Find the indefinite integral. (a) / (2* + v#)dx (c) / 2x6 + x5 -dx x4 (4) [(4cs (xỉ + 5x + 4)dx (4…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Find the area of the shaded region. x = -y x = 2 – y? -2 2 10 В

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Q: Solve the following differential equations: . 2y ++ e* (1+) dx + (x+ 2y)dy = 0.

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

A: Solve the following

Q: Find the area of the region shared by the cardioids r= 12(1 + cos 0) and r= 12(1 – cos 0). The area…

A: Given: r=12(1-cosθ) r=121+cosθ

Q: Find the area inside the oval limaçon r=7+3 sin 0. The area inside the oval limaçon is (Tuno uor…

A: we have to find the area.

Q: In which limits below can we use L'Hospital's Rule? x – 2 lim 1→2 In(3 – æ) 1- et lim 2-0 sin(5x)…

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Q: Evaluate the directional derivative Duf (3, 4) if ƒ (x,y) = /æ² + y² and u is the unit V vector in…

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Q: Find V· (V × F), if F(x, y, z) = e®²i+ 4xe®j – 5eV²k. V.(V × F) =

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Q: y =x und y = x+2 ... evolve the area about the line x 3. Using cylindrical shell method, the volume…

A: The cylindrical shell method gives the ,Volume on revolution about a line is given by…

Q: 15x + 44 -5x + 84=26 then astructions: Rewrite each Systems of equatons as amatrix, perform cow…

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Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: The arc y = x² from (0,0) to (2, 4) is rotated about the y-axis. Find the area of the resulting…

A: We want to find surface area

Q: Find the constant a, such that the function is continuous on the entire real line. ( 2x², f(x) = if…

A: Given the function is f(x) = 2x2,if  x≥1ax-1,if  x<1

Q: Evaluate the line integral. The simple curve is C is y = x² starting at (0, 0) and ending at (1, 1).…

A: We can solve as follows

Q: 1. For the curve x2y2 = 25 at (-1,-5), find the equation of the normal line.

A: The given curve is: x2y2=25 Differentiating it with respect to x: y22x+x22ydydx=0 at (-1,-5):…

Q: Find the area of the shaded region. y = x² +1 %3D 5 y = x -1 A 23 2. 2/2

A: Given

Q: Area Between Two Regions Name: (a,h) (0, 0) (b,0) Use integration to determine the area of the…

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Q: 24) use the Refio Test to determine tue canvergen ce or divergence of tue seri's 7n (~1)"(4)'…

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Q: Find the length of the curve. 9) The spiral r = 202, 0 s 0 s 2^/3

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Q: 3 roblem 4. The third term of a geometric sequence is 9, and the common ratio is Find the fifth…

A: Given problem:- The third term of a geometric sequence is 9, and the common ratio is 3/2   Find the…

Q: Consider the function f(x) = cos(3 x). (a) Give the derivative of this function. f'(x) = | (b) Find…

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Q: The area of the region is. (Type an exact answer, using x as needed.)

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Q: Problem 3. at a speed of 60 cm/s. Suppose the function g models the radius as a function of time t…

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Q: The function f(x) = 2x° 39x + 240x – 11 has two critical numbers. The smaller one is x = and the…

A: Topic = Derivative

Q: Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x² – 3x + 8…

A: Here We have to use the definition of the derivative.

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: ind 4 using implicit differentiation and evaluate the derivative at point (-1,2) 2.a°y + 5x?y³ = 2x

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Q: Evaluate the limit V5 + 7x² lim 5 + 4x I+ 00

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Q: Problem 7. Solve the equation logx+log(x+1) = log12 and leave your answer in exact value.

A: Topic = Algebra x=3

Q: Give inequalities for r and 0 which describe the region below in polar coordinates. (Click on the…

A: Angle is given by arctan(y/x)

Q: Find the derivative of: 3 sin (– 3x). Hint: sin (x) = [sin(x)]"...so use the chain rule (twice!).

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Q: 15. Find x² (2x³ + 4)5 dx

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Q: Use L'Hospital to determine the following limit. Use exact values. In r lim glnz

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Q: 7. An analyst has found that Tom's Transmissions Company cost function is: C(x) = 40,000 + 500x –…

A: Marginal cost =C'(x)  To maximize or minimize use double deriveative test