Find the limit. lim (t i 6 j + t² k) t-5 lim (t i − 6 j + t² k) = i t-5 i+ i j+ i k

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A: Value of x for which series is convergent is given.

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Q: r = 12 sin 18ti + 12 cos 18tj

A: Given :

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Q: Use Green's Theorem to evaluate the line integral Jo (y - x)dx + (2x - y)dy for the given path. C: x…

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Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

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Q: Given: xy =tan(x - y). Find dx/dy. tan² (z-y) soc²(z-v) +tan² (z y) sec (x−y) -sec² (2-y)-z 當…

A: find derivative dxdy from equation xy=tanx-y

Q: 6- Write four examples about sketch the graph in polar coordinates from families of cardiod and…

A: Let's find.

Q: ind r'(t), r"(t), r'(t) r"(t), and r'(t) x r"(t). r(t) = 2t²i - 2tj + 5t³k (a) r'(t) (b) r"(t) (c)…

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Q: Write the Taylor series for f(x) = x³ about x = −2 asen(x+2)". n=0 Find the first five coefficients.…

A: Given that      f(x) = x3

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A: Find dz

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Q: (1) What is the approximate volume of a thin cylindrical shell with height 2, radius 3, and…

A: Solution ) Volume of the cylinder    V = πx2h        x = radius         Differentiate with respect…

Q: 3. Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that has a…

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Q: Evaluate the line integral ſ F. dr, where F(x, y, z) = sin x i + cos y j + xz k, where C is given by…

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Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (1, 4)…

A: As per Bartleby guidelines I have authority to answer only one question. If you want other…

Q: (D²4)y= 8e²x - 12

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Q: ³ _ x + 2y x-2y find first derivative X = to

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Q: Set up the definite integral required to find the area of the region between the graph of y = 19 -…

A: area between curve

Q: Ex. (7) Sol:- Solve y" +y'+y=6sin (2x) ➤ For y y"+y' + y = 0 Homogeneous [6sin (2x)=0] m² +m+1=0 1…

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Q: 3. Write down the name of the conic given by the polar curve r = 6/(2-sine). Determine the vertices…

A: Given problem:- 3Write down the name of the conic given by the polar curve r = 6/(2-sin(θ))…

Q: trignometric

A: We will find the solution.

Q: (a) Find the acceleration of the body each time the velocity is zero. Enter your answer as a list if…

A: Follow the procedure given below.

Q: A new fish species is introduced into a lake. Assuming that the population of fish quadruples in the…

A: Solved below

Q: Evaluate [x²z dx - yx² dy + 7 dz along the curve C shown in the figure. с 4 X [x²zdx - yux²2 dy +7…

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Q: Evaluate F. dr along the curve C if F(x, y) = (x² + y²)¯³ (xi+yj), с and C: r(t) = et sin ti + et…

A: F.dr is integrated along the curve C.

Q: (D² − 4)y : 4)y = 8e²x - 12 Your answer

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Q: Find the volume of the solid obtained by rotating the region under the graph of the function f(x)…

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Q: Let f(x)=x2+2x-1 and g(x)=2x-4. Find 3f(x)-2g(x)

A: Given fx=x2+2x-1 & gx=2x-4 To find 3f(x)-2g(x):

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Q: the vector-valued function.

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Q: The smaller the curvature in the bend of a road, the faster a car can travel. Assume that the…

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Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

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Q: 3. Evaluate the line integral Sc F. dr where F(x, y, z) = (e², xz, (x + y)) over the curve r(t) = t²…

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Q: If In a 2, ln b = 3, and ln c = 5, evaluate the following: = (a) In (10-2) = b-4c² (b) In √6-³c-²a-1…

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

A: We know, ddtr1(t).r2(t)=r1(t).dr2(t)dt+r2(t)dr1(t)dtddtr1(t)×r2(t)=r1(t)×dr2(t)dt+dr1(t)dt×r2(t)

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Q: An air traffic controller spots two airplanes at the same altitude converging to a point as they fly…

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Q: y" + 6y' +5y=10sin (2x)

A: First find AE(Auxiliary equation) and PI ( Particular integral)  then CS ( Complete Solution) is PI…

Q: Change the polar equation 2r = 2 + cos 0.(2r - 1) to Cartesian equation

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Q: Let G₁ be z = 6-√√36 - x² - y² and G2 be the upper nape of x² + y² - 3z² = 0. If S is the circle…

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Q: 16. Let u = ln t, t = 2r and r = √w. Find and simplify du dw in terms of w.

A: As per Bartleby guideline,  we have answered only the first question. Please repost mentioning the…

Q: A table of values of an increasing function fis shown. X 10 14 18 22 26 30 f(x) -11 -5 -2 1 5 Use…

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Q: If f f(x) dx = 12, then ff(4x) dx is equal to If f f(x) dx = 12, then fx f(x²) dx is equal to

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Q: Find c> 0 such that the area of the region enclosed by the parabolas y = x² − c² and y = c² – x² is…

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Q: Use the form of the definition of the integral given in this theorem to evaluate the integral. [²4x³…

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Q: = Write the Taylor series for f(x) Find the first five coefficients. Co= C1= C2= C3= C4 e about x =…

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Q: Solve for the solution of: (D2 - 4)y = 8e2x - 12

A: Given problem:- Solve for the solution of: (D2 - 4)y = 8e2x - 12

Q: Find the interval of convergence of n²x³n 33n n=1 interval of convergence = (Enter your answer as an…

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Q: Solve the following differential equations of y"-2y' +24y=3sin(4x)+6cos (7x)

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