Question 16 Find the equation of the tangent plane to the given surface at the indicated point. x2 :(3, 3, 4) O1 1 O 3 3 O1 1 O1 1

Q: Find the area bounded by the curve r= 2+cos θ

A: Given problem:- Find the area bounded by the curve r= 2+cos θ

Q: Solve the following differential equations of dy 1 y= xy'; dx x

A: To solve the following differential equation

Q: Evaluate each integral. dr 1. VI² – 1 2. [zcos I Cos az dz 7x +1 dr 2-- 2 3. 7 – I – z

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t→+∞\ 5t2 +6' 8t (?, ?)

A: To evaluate the following limit.limt→+∞t2+85t2+6, 18t=?, ?

Q: Solve the following differential equations of dy 1 -·y = xy'; dx

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Q: Solve the differential equation Integrating Factor by Linear Equation: dx + xcoty = ecosy dy

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Q: Solve the differential equation. dr sin 0- do +(cos 0)r = tan 0, 0<0<,

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Q: Calculate ri(t) · r2(t)] and r.(t) × r2(t)] first by differentiating dt the product directly and…

A: This is a problem related to dot and cross product of vector. Based on the general formula and…

Q: -x lim + 169 x→-9 x+9

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Q: =/2 4. cos z dr Jo da 5. I+1 I +IA

A: We have to evaluate the indefinite integral

Q: Solve the following differential equations of dy x'y-x'. = y' cos(x). dx

A: Use substitution to reduce the differential equation into linear differential equation.

Q: E(-1)" n n=1

A: Series

Q: Solve the following differential equations of yy' + y' = x;

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Q: 6. lim (sinx)* X0+

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Q: 6. lim (sinx)*

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Q: 7. Solve the general solution of DE: y" -5y' + 4y = 3e%r O y = cje" + c2et* + er 10 O y = cje* +…

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Q: 2.) f x²(2x³ + 1)5dx

A:

Q: 4. dr 4-

A: Given: ∫02x34-x2dx

Q: 3.) ž sin'(x)dx

A:

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A: We have to find the values of vector valued functions.

Q: lEvaluate the integral ×+ス de . x²+2x linlx?Cx+z)e X+2 (x+2)²|&7C Dinlx (x+2)I +c E) Inl x て) 12

A: Topic = Integration

Q: Find the Taylor series for f(x) centered at the given value of a. [Ass f(x) = In(x), a = 6 |(-1)*+1…

A: We can solve this as follows:

Q: x³ Jx² +3dx

A:

Q: 1.) Find the area bounded by the curve y?= 1 - x and 2y = x + 2 2.) Find the area bounded by the…

A: Solution is given below:

Q: Find curl (3z i + 4x j+ 7y k). curl (3z i+ 4x j+ 7y k) = ( i )i + ( i j+ ( )k

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Q: 7y" – 5y' – 2y = 0 ; y(0) = 4 ; y'(0) = 0 |

A: differential equation

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

A:

Q: A forest has a population of cougars and a population of rabbits. Let æ represent the number of…

A: A detailed solution is given below.

Q: ) Sypposef and g are functions with continuoUS elerivatives, and that they satisty the following. is…

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Q: Question 4 of 4 y = (x³ – 3x²)(x² + 4.x + 2)®

A: A detailed solution is given below.

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

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Q: Solve the following given differential equation  using the method of indeterminate coefficients

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Q: dy For each of the following functions determine dr

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Q: Compute the given improper integral. Enter the exact value of the answ 13 1 dx x² – 25

A: Here we have to find the exact value of ∫5131x2-25dx=?

Q: Solve the differential equation Integrating Factor by Linear Equation: y' + X. (4)» = * y = x+

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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: 5. lim X-0 e2x-1

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Q: 2) Evaluate the integral S inx dr 2.

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Q: Solve the differential equation Integrating Factor by Linear Equation: dy — у — 5х* — Зх? + 2х — 0…

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Q: Evaluate the double integral. / 5x(4 + y) dA; R R is the region in the first quadrant enclosed by y…

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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: Solve the differential equation Integrating Factor by Linear Equation: y' = 1 – 2ycot2x

A: We can solve this as follows:

Q: Follow the instructions. Typewritten for upvote.

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Q: (2y²+ x²+3 0. प्रमत्ण ै

A: This is a problem of double integration. Based on the general formula we will evaluate the integral.

Q: dy For each of the following functions determine da

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Q: B)号 4. nこt u puyと いつ0o Sinlen)+ w!l いo an

A:

Q: 2. lim (ex – 1)lnx X0+

A: (2). The given limit is: limx→0+ex-1lnx As we know that, the second indeterminate form is: ±∞±∞ ;…

Q: 1 f. dx Vx(Vx + 2)

A: Find your answer below

Q: Find the integral | 2(x* – x°)(x5 – 1)®dx а. b. In x2 dx 2х J x + 3)* С. 5.

A:

Q: A company is planning to manufacture snowboards. The fixed costs are $400 per day and total costs…

A: Cost