Use the first six non-zero terms of the Maclaurin series expansions for sin x and cos x to approximate the values of sin π/12 and cos π/12. Compare your results withresults you obtain from your calculator. (Make sure your calculator is in radian mode.)

Q: Find the equation of the tangent plane to the graph of f(x, v) = In (17x² – 14y²) %3D at the point…

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Q: Help Homer design a cylindrical silo to hold the output from his pet pig Harry Plopper. The silo…

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Q: L, f(x)dx + [° f(x)dx = 5. Si f(x)dx – Sº f(x)dx = 4.

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Q: ||r'(t) x r"(t)|| Use the formula k(t) : to find k(t). 3 r(t) = ei+etj K(t)

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Q: Assume that f(x)dx = 3 and g(x)dx = -2, find the following: 1. Sf(x) + g(x)]dx = 2. S12f(x) – g(x)]…

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Q: R be the region bounded by the curves y = 10 − x^2 and y = x^2 − 8x. Set up, but do not evaluate,…

A: Given query is to setup the integral for area .

Q: an

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Q: n² < 2" for n = 4,5, 6, ... (Hint: 2n + 1 < 2" for n = 3,4, 5, ...)

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Q: 3+ 12x4 – 7x +x³ a) lim 2л2 — За3 + х — 424 3x3 +x – 4x4* - -

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Q: A swimming pool is circular with a diameter of 40 feet. Depth is constant along east-west lines and…

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Q: Inx 6. lim,

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Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

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Q: Find curl (4z i + 5x j + 3y k). Exact number, no tolerance. curl (4z i + 5x j+ 3y k) = (i )i + ( )j…

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Q: [2.xyy' – y² +, Vy* +x* ; 4– %3D

A: ∫x2+a2 dx = xx2+a22+a22lnx+x2+a2+C

Q: Write the expression as a single Integral -3 1. Sf f(x)dx + S, f(x)dx = -3 - 3. S f(x)dx + S, f(x)dx…

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Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x? b.…

A: area under the curve

Q: (2xy+x^2+x^4)dx - (1+x^2)dy=0 the answer should be

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Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. 2(3*)…

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Q: Change the order of integration. f(x, y) dy dx Jo

A: 0≤x≤10≤y≤xRegion bounded by:x=0, x=1y=0, y=x

Q: Prove that n2 +1 > 2? when n is a positive integer with 1<n<4.

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Q: mparison test to determine whether the given series conve:

A: Please refer to the image below

Q: 2ln|x| + 3 ln|x + 1| – * - + C 5x2+11x+2 dx x(x+1)2 2ln|x| + 3 In|x + 1| ++C 4 2ln|x| + 3 ln|x + 1|…

A: Given: I=∫5x2+11x+2xx+12dx   As we know that; The Power rule; ∫ax+bndx=ax+bn+1an+1+C And…

Q: :. Let x(t) = 2 sinh t , y(t) = cosh(t²) be a curve in the Oxy-plane, given in parametric form. (a)…

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Q: Find div F and curl F if F(x,y, z) = xzºi+ 5y°x²j+ 5z?yk.

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Q: Find the J(2x + 1)³ dx

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Q: 6. Find the indefinite integral. S 3x³ V3x4 + 7 dx (Use substitution method)

A: Solving the problem by finding the value of integration.

Q: o<×くT ② Foのコ 2 [:

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 5…

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Q: he curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i + 4 sin(t)j + tk; t 2…

A: Please refer to the image below

Q: (a) Use Green's Theorem to find the line integral over the simple, closed curve C : r(t) = (cos t,…

A: To use green's theorem to find the given line integral over the curve C

Q: 2. Find the 11th term of the following geometric sequence. 4, 12, 36, 108, ...

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Q: Evaluate the line integral -ydx + xdy along the curve C C : y? = 15x from (15, 15) to (0, 0). NOTE:…

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Q: Find the length of the curve r (t) = i + 6t°j + 2t°k, 0 <t < V1 L =

A: We will find the length of curve.

Q: Solve [D* +3D² –4]y= 2sin° (5x)

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Q: 14th term of the following geomnetric sequence. Find the 1. 2, 4, 8, 0. 昌 唱

A: Use geometric series concept

Q: Find the S(x* +) dx xe-1 А. 1x? + c e-1 4e xe+1 В. Ix2 + c e+1 2e xe+1 С. 1x3 + c e-1 Зе xe+1 1 D.…

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

Q: 22. u = Vr² + s², r = y + x cos t, s=x + y sin t; ди ди ди əx’dy when x = 1, y = 2, t = 0 dt

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Q: Use the One-to-One Property to solve the equation for x. 3x - 1 = 27 %3D X =

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Q: If 1 f(x) 1 .3 + 1 + x 4 X° + 3 then find f'(0) +

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5- 5 -5+ -5+

A: Given data÷

Q: Given the curve v = x3 – 3x find the stationary or turning point

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Q: sin x – 2+ csc x (c) sin x – 1 sin x CSc x sin x + 1 | 1 (d) cos(tan-l x) = V1+ x² 1+cos u (e) Using…

A: We have to answer following Questions.

Q: 3 + In?x dx

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Q: i(x) = 2-0.8(x-43.79)

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

Q: H.W (5) Solve the following differential equations of (3x -6xy)dx+(-3x' -2y)dy 0

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Q: +2x-15 Inkx + 51 -inlx- 31 +c In]x+51-Inx- 31+C Option 1 Option 2 |(x + 5)°| +C (*+5) +C *-3 Option…

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Q: dy 2 + y = 0, y(0) = -3 dt

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 3. Vdx + (2x +1 – Vx)dV = 0

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Q: Evaluate lim (x)/

A: We can find the  limit as below.

Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. 2x-5 =…

A: Given data:- 2x-5 = 16