NAME: 1. Decide (with proof) convergence or divergence of the series .(d), find the exact sum. 1) Enzi 3n+5 7n

Q: 13x + 6/3xy + 7y² – 80 = 0 %3D

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Q: 2xージ f (x) : 33 Vx2 T sin 2x + Ve2x + 2x –- In e, x # 1 1-x (1–3t)5(t³-8) g(t). t # 2 2-t

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Q: dx Evaluate: ²+4 x² + 4 – 4 + C +4 +4 | A In B None of the given choices in V x2 +4 - 2 + C C) x² +…

A: The integration of the integral is 1/[x sqrt(x2+4)].

Q: Question 11 |In |25- x² -dx , if we let u=V25- x² , then udu= - xdx. T True F False

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Q: Consider / sin'x cos²x dx. jf we let " =cos x , the integrand can be transformed to , O J(- 2u?- u*…

A: The given integral,    ∫sin5x cos2x dx

Q: Determine whether Rolle's Theorem can be applied to f on the dosed interval [a, b]. (Select all that…

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Q: Find the derivative for each function be low at x=1 a) flac) 6) fla) = 2(x-1)5 %3D Vox2+1) e ) fx) =…

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Q: S sec°x tan x dx +C + C sec³x + C

A: ∫sec5x tanx dx=∫sec4x (secx tanx) dxusing formula∫fn(x) f'(x) dx=fn+1(x)n+1 +cHere , f(x)=sec4x ,…

Q: V9-x² 2. dx. Use trigonometric substitution. x2

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Q: If R is the region enclosed by 36 – 4x? - 4y² = 0 and 2x + 2y?- following sets gives R in the polar…

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Q: Use a graphing utility to graph the function and find the absolute extrema of the function on the…

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Q: csc*n y 7. S dy cot²n y

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Q: Find the values of a and b for the curve x'y+ay =b if the point (1,1) is on its graph and the…

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Q: | Find the minimum point for the function f(x) =1 + 12x – 4x (2,-7) (0, 1) Oa.9) (1, 9) O (-1, -7)

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Q: (a) Find the unit vector having the same direction as B- A+ 2C. (b) Give the direction angles of B-…

A: We have to solve given vector Questions

Q: The line through (- 10,7,10) perpendicular to the plane 9x + 2y + 6z =5 Choose the correct answer…

A: Given query is to find the equation of the line.

Q: u+ 2v 4] = 1+ vw; w, and vw. w

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Q: If D is the region enclosed by 4 < x? + y? < 9 and y <0, then which of the following is the setting…

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Q: Find:  ∫cosh^4 (x) sinh^5 (x) dx.

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Q: Evalute the indefinite integral

A: To evaluate the integral.

Q: Sveluate esing Sub method 7.

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Q: When J x°cos (x-)dx is evaluated using IBP, the value of J v du is? A - cos (x2) B none of the…

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Q: 1 Y(s) : s2 + 7s + 10 a. y(t) =(e-5t – e24) b. y(t) =(e-5t + e²') c. y(t) =(e5t - e-2t) d. y(t)…

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Q: Sketch the region of i nd change the order of integration ntegral 9. 3 f(x, y) dydx

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Q: Use the method of Lagrange multipliers to find the maximum and minimum of f(x,y) = 5xy subject to x…

A: We have to find the maximum value.

Q: Veluate lesing Sub methad s x(xZ-3)" dX 1

A: Given query is to find the integral using substitution method.

Q: Find the derivative. (The Fundamental Theorem of Calculus -- Part 1) 19) y = cos ft dt COS-

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Q: Consider J sin'x cos²x dx. If we let "=cos x , the integrand can be transformed to. A 2u2 - - | (u²-…

A: The given integral,     ∫sin5x cos2x dx

Q: Find the absolute extrema of the function on the closed interval. h(s) = [0, 2] %3D s- 3 minimum (s,…

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Q: If y = x + ex, find dx/dt.

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

Q: 1 In solving the antiderivative of f(x) = 2 - sin(x) by miscellaneous substitution, the substitution…

A: Here we have to use the subsitution.

Q: (4t³ – e') dt

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Q: Finding the Slope of a Graph In Exercises 23–26, find the slope of the graph of the function at the…

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Q: 5xy = 4x²z – 3yz2; yx and y,. -

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Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A: This question can be solved using the concept of rate of change of physical quantities.

Q: In²(x3) 26) dx A) 192 B) 192e3 C) 1728

A: We will use substitute method to solve the integral.

Q: The owners of a restaurant are interested in analyzing the productivity of their staff. The function…

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Q: Question 1 1 In solving the antiderivative of f(x) = sin(x) + 3cos(x)+3 by miscellaneous…

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Q: cos(x) 1- cos(x) by miscellaneous substitution, the substitution z=tan In solving the antiderivative…

A: Here we have to use the subsitution.

Q: S tan³ 6x sec10 6x dx 1 sec1²6x + sec1º6x + C 72 1 60 B none of the choices 1 -sec1²6x + 72 1 1…

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Q: smoving along the graph of the given function at the rate ax/dt. Find dy/dt for the given v - = 2x +…

A: Given query is to find the value of indicated derivative.

Q: S tan³ x sec x dx sec3 x - sec x + С none of the choices sec³ x + sec x +C 1 sec3 x + sec x +с В

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Q: For the integral, / tan'x sec*x dx, if we let u = tan x, what is the re-written form of the…

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Q: y' = et ; y(0) = 2 find the general solution

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Q: f'(x) = cos x; y (G) = 3 %3D

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Q: S sec?x csc²xdx O None of the choices tanx + cotx + C O - tanx + cotx + C O - tanx - cotx + C O O

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Q: 1) Ifféx) =x + 5 and g(x) = x² -3, then find g(Ư(0) . 2) Iffés) = secx, and g(x) = L, then find…

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Q: A/ Certain values of x and log1o x are (300, 2.4771), (304, 2.4829), (305, 2.4843) and (307,…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: End P4)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Consider the function f(æ) = 10,/T + 7 on the interval [2, 10]. Find the average or mean slope of…

A: This question can be solved using the concept of mean value theorem.