Find the area, A, of the region enclosed by the cardioid r = 8+8 cos 0.

Q: Find the area bounded by the curve y = 9 - x2 and the x-axis. a) Horizontal Strip b) Vertical Strip

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Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). ||r(t)||° r(t) = e#i+ etj K(t) =

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Q: 7. lim vx2 + x + 1 – Vx² + 1 ズ→0

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Q: INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) F(x) f'(x) lim = lim Еquation…

A: This question is based on L hospitals rule.

Q: Evaluate the integral / (12x + 18y)dx + (12x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: 1. Given the General Solution the DE, Identify the roots * y = C1e4* + C2e¬* + C3 O A) m1= 4; m2= 0…

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Q: 2.) f x²(2x³ + 1)5dx

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. 2…

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Q: 5 6 2 16 41 If =2 4 1 and B-3 3. find the sum of AB. 3 3 2

A: Matrix ab

Q: )Solve for k such that 1 k(x2 – 2x + 1)dx = 5 - 0.

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Q: Describe the domain and range of the function. f(x, y) = 3x2 – y Domain: O (x, y): x = 0, y = o…

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Q: Use the formula r(t) - – P) x r"(0)|| to find giớ). ||P() × to find x(t). r(t) = e!l"i + e tj 156…

A: Given problem:- Find k(t) of r(t) =e12t i +e-t j

Q: y = 3x - x² and y = 2x %3D

A: See the details solution in below

Q: 5. lim X-0 e2x-1

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Q: f(9(x)) = 5 (x + 4) 2 f(g(x)) = (2a² + 3x – 5)7 f(g(x)) = (3x – 1)25 1. - 3.

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: A lighthouse is on an island 250 meters off shore. The lighthouse beam makes a full turn every 7…

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Q: Let 7 (t) = %3D Find F'(t) F(t) - « Question Help: D Video Add Work Submit Question

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Q: Given the function: x² –4 if x + 2 f(æ) = { k, 2-x if x = 2 What should be the value of k so that…

A: We have to find value of K

Q: Let 7(t) = Find a parametric equation of the line tangent to 7(t) at the point (7, 5, 1.386) x(t) =…

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Q: Evaluate Soni Sm e" sin(e")e dædy cIn 1

A: Integral

Q: The linear system with corresponding augmented matrix 2 -1|4 is consistent. True False « Previous…

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Q: -x lim + 169 x→-9 x+9

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Q: Determine the vector field of F. (x, y) = 12i – 4j 1

A: given isF(x,y)=12i-4jgraph of vector field of F is attached below

Q: b. S 2*³-4x²-x-3 dx х2-2х-3

A: First we divide the polynomial  using long division

Q: dy For each of the following functions determine da

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Q: Obtain the limits of the following functions: (2sinx-sin2x 1. lim x-sinx

A: To evaluate the limit of the function.

Q: Find V × (V × F) if F(x, y, z) = 9xyj+10xyz k. V x (V × F) =|

A: We have to find given expression.

Q: Q6 Find dy, if y= +++

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Q: Find curl(7z i + 8x j+ 5y k). curl (7z i + &x j+ 5y k) = ( i )i + (i )j + ( )k

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Q: Solve the general solution of DE: y" -5y' + 4y = 3e6r O y = cje* + c2er + ner 10 y = cje* + czet* +…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. 18.% I cos(m2") dy dz

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Q: If f (x) : 2, what is the equation of the line tangent to f(x) at x = –1? O y+24x + 36 = 0 O y – 24x…

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

Q: Which among the choices is NOT true about the continuity of f(x)? x2 -4x-5 if x + 5 f(x) = 2x–10 3,…

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Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: Solve the differential equation Integrating Factor by Inspection: (xy – 2y?)dx – (x² – 3xy)dy = 0

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Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to…

A: For the arc y = x2 and the range of x from 0 to 1. So, dy = 2x dx. Now,…

Q: Using appropriate substitution 9x2 – 4 dx X is equal to

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Q: 2. Determine the area of the region bounded by the curve y = x3 – x2 – 2x, and а. the x-axis

A: This is a problem related to finding out are using integration. Please follow the procedure given…

Q: Find T(t) and N(t) at the given point. r(t) = (t – 5)i + tj; t= 5 T(5) N(5) =

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Q: 7. lim vx2 + x + 1 – Vx2 + 1

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A: greens theorem

Q: Line segment AB is a diameter of the x² +y² + z² - 2z + 8y = 9. Find point B if A = (0, у, 0).

A: To find the point B if Coordinates  of A are given for the sphere.

Q: O f(-1) = 3, lim f(x) = 3, lim f(x) = +∞ O f(-1) = 3, lim f(x) = -o∞, lim f(x) = +o0 O f(-1) = 1,…

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Q: Verify Green's Theorem by evaluating both integrals y² dk + x² dy = / dA ay ax for the given path.…

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Q: True or False. Explain your answer The limit of sin(x) as x approaches very large values is 0 or 1.

A: Given

Q: 4 f (g(x)) = (3x² – 2x + 4)6 f (g(x)) = (x)(x² + 3)² - 5.

A: We have to find derivative of given function.

Q: Hi there, please help me with answering this question. I am a bit confused here. It would be highly…

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Q: -Find Taylor or Maclaurin for the following functions: 3) 2) f (x) = e* at a = 2

A: A detailed solution is given below.

Q: Determine the equation of the tangent plane and normal line to the surface at the given point.…

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Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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