Find the limit. lím (t i – 3 j+ t2 t+2 lim (t i- 3 j+? k) i+ j+ i i i

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A: Vertex ( -3 , 2 ) covertex ( -1 , -1.5 )   Center= ( h , k )= ( -3 , - 1.5 )   Major axis b = 2 - (…

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A: We have to find the solution of  integral

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A: Given (5x2 -y)dx + xdy = 0 (5x2 -y) + xdydx = 0 Calculate whether the differential equation is exact…

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Q: Use sigma notation to write the sum. 7n 7n Σ I = 1

A: To use sigma to write the sum.7n6-7n7n+...+7nn6-7nn7n

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A: To solve the following problem

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Q: ||P(t) × r"(t)|| Use the formula «(t) to find x(t). r(t) = t²i + t³j K(t):

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Q: Evaluate (x - 4y + z) ds. S: z = 5y, 0 s x s 4, 0 sysx

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A: According to the company rule we can answer only first question and rest can be reposted.

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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Q: x³ + x² + 2x+1 dx (x² + 1)(x² + 2)

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Q: SOLVE THE EQUATION. SHOW YOUR COMPLETE ANDCLEAN SOLUTION. (x – 2y + 5) dx - [2 (x – 2y) + 9] dy = 0…

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Q: Evaluate the integral (Partial Fraction Decomposition) xdx J (x2 + 2)(x² + 1)²

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Q: Evaluate ||e+ dA where D is the triangle with vertices (0,0), (-2,4) and (8,4). D

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A: Solution is given below:

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Q: t-4 lim x-3-3-ax

A: We have to find out the limit

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A: Given query is to find the value of a and b.

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Q: А. f(x) 3D Vx + 1; а %— 6 if x > 1 if x < 1 a = 2 С. f(*) — 13х + 1l; а %—-+ a = (3х — 2 В. f (*) —…

A: Only Function given in (C) is continuous at that point but not differentiable at that point. For…

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Q: Evaluate the integral. 1 (4 + r)3 dr

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Q: Find the area of the shaded region. y 14 y= 7x- x² 12 10 (5, 10) 6 4 2 y=2 x 2 4 6 8 CO

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Q: A problem or equation of the tangent line to a curve at the point (1,3) is y = x+2. If at any point…

A: Let's find.

Q: ,00 is deposited in an account with an interest fate of 1200 ) ith respect tor when r is 10.00%. dA…

A: Given query is to find rate of change of amount with respect to r.

Q: 1.) Determine the largest interval over which the function flx) = \x+3 is continuous. 2x 2.)…

A: 1) To find the largest interval on which the function f(x)=x+3 is conitnous.

Q: Use the formula k(t) = ||r'(t) × r"(t)|| to find k(t). ||r(t)||* r(t) = 8 cos(7t)i+8 sin(7t)j + 3tk…

A: Let's find.

Q: Prove the given identity. tan0 + cot0 = csc@sec®

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Q: Find the general solution of (3xy-y²)dx-(x²-xy)dy=0

A: As the equation is homogeneous , put y=vx and solve .

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Q: 17. у dx — (х + бу?) dy 3D0 (х + бу?) dy %3D 0-

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Q: 5x - 4 dx x3 + 4x2

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Q: Find the area of the region enclosed by y = 5x and x = 6.5 - y. 2- 3 4 5 6 Use horizontal strips to…

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