Find the area of the surface obtained by rotating the curve of parametric equations T = 2 cos 0, y = 2 sin3 0, 0 <0 2 !!

Q: Find r'(t). r(t) = (tan-'(5t))i+t cos(t)j – Vik NOTE: Enter your answer in terms of i, j, and k.

A: r(t)=tan-1(5t) i+t cost j -t kddt tan-1(5t)= 11+(5t)2 ddt(5t)ddt tan-1(5t)= 51+25t2 ddtt cost=cost-t…

Q: Given function:  f(x) = 4x^3 - 7x^2 + 2x - 5 A. Find the exact x & y coordinates of stationary…

A: Given: f(x)=4x3-7x2+2x-5

Q: If f is just that = e*[- sin(x + y) + cos(x +y)] and -e sin(x+y) which if the %3D ay following is…

A: On solving this we will get:- Option (A) is correct.

Q: Find curl (3zi + 4xj+ 5yk). curl(3z i+ 4xj+ 5yk) = ( i )i + ( i )j + ( i )k

A: We will find the curl.

Q: For AABC, you are given mZC = 123°, mZB = 44°, a = 11ft. Find c. 40 ft 44.2 ft 41 ft 38 ft Previous

A:

Q: rrent Attempt in Progress Find r'(t). r(t) = (tan-'(9t))i+t cos(t)j – v NOTE: Enter your answer in…

A: We have to find the derivative

Q: Find [r(t) · u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = ti + 8t2j + t³k, _u(t) =…

A:

Q: roduct directly and then by applying the formulas dr dr r(t) and dt dr, dr x ). dt Fi(t) - cos(t)i +…

A: To differentiate.

Q: 3.

A: ∫x41-x2dxPerform trignometric substitutionSubstitute…

Q: SUTM i) Find the domain 1. Given z = f(x, y) = /36 – 9x² – y-. of the function. ii) 3 UTMd rano UTM…

A: Let's find.

Q: dy cos (x) cos (Y) %3D da O a. 2 In sec (3) +tan (3)| = %3D O b. 4 In sec (3)) + tan (y) %3D

A: Given: dydx=cos2x cosy

Q: Use the Rules of Differentiation to differentiate the following functions: a. f(x) = 2x³+ 6x d. h(x)…

A: Given data

Q: (D2 – 1)y = 2e-*(1+e-2*)-2, %3D

A:

Q: S csc° 3x dx

A: This question is related to indefinite integration, we will we will solve it using given…

Q: 8. Find the limit: lim E1(1 130 noisieoq Isisinle bna baoes 1aq d00

A: The detailed solution is given below Thank you

Q: Using (sin x) = cos x and (cos x) = – sin r dr dr Show that # (cot x) = - csc² x dr

A: We need to show that ddx(cot x) = -csc2 x Given ddx(sin x) = cos x and ddx(cos x) = -sin x

Q: 1. Let -1 -5] 3 -7 3 -6 -3 A = B= 6. 5 -3 -2 4 2 | -3 Determine which (if any) of the following…

A:

Q: Find div F and curl F if F(r, y, z) = xz°i+ 2y°x²j+ 6z²yk div F= 2° + 16 y' x + 12 z Y curl F=

A: Given F(x,y,z)=xz6i+2y8x2j+6z2ykTo find div F &amp; curl F:

Q: Use Stokes's Theorem to evaluate F. dr. In this case, C is oriented counterclockwise as viewed from…

A:

Q: dt 1-cos t+sin t

A: First we shall simplify the expression then integrate

Q: Problem 5 Part 1: Consider a cost function where C(x) in Philippine peso is the total cost of an…

A: Let's find.

Q: Apply

A: We will solve the integration.

Q: 3/2 x*(G²- x²) %z

A: …

Q: dx sinxtanx

A:

Q: Let v=f(x) be a solution of the first order linear differential equation y'=y-10x² such that f(0)…

A:

Q: y = Vx + 3 from x=1 to x=4

A: We find the area under given curve and bounded by axis and given lines x=1 &amp; x=4 using definite…

Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) =…

A:

Q: Find V (V x F) if F(x, y, z) = 8 sin xi + 6 cos(2.x - 3y)j + 7zk. %3D | V. (V x F) =

A:

Q: 26) find the mternel of convergenu of tue power Senies (x-6)*-1 и -) 6 onsurs : aj (6,l2) d) (-6,6)…

A: A detailed solution is given below.

Q: Find the divergence of the vector field F. F(x, y) 4xe*i 6x²y?j

A:

Q: Evaluate the following limit using Taylor series. 7 7 tan 1(x) – 7x+: lim 4x° 7 .3 7 tan (x) – 7x +…

A: Given problem:-

Q: S 2y(yª – 4)¯³ dy

A:

Q: Find the Yalue + Cas

A: Using inverse trigonometric formula achieve this expression

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating d dt' the product directly…

A:

Q: F. Change the Cartesian integral to polar coordinate 11-y !! (x² +y*)dx dy

A:

Q: 1. Calculate the following limits (showing all working): log,(n) + 5" n-0o log7(n) + 7" Vn5 + 2 +…

A:

Q: Find the constant a, such that the function is continuous on the entire real line. ( 2x², f(x) = if…

A: Given the function is f(x) = 2x2,if  x≥1ax-1,if  x&lt;1

Q: Evaluate the definite integral. + ej+ dt - 1) i - (e" - 1) j +k O e? i+ (e-1-1) j+국k 2.

A:

Q: : Consider the differential equation xy" + 3xy – 3y = 3x2 – 2x. %3D = x -3 (a) Verify that y1 = x…

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). %3D 13 r(t) = ti + t5j K(t):

A:

Q: 15. Evaluate the following double integral. Si (xy* + x)dydx

A:

Q: Evaluate the definite integral. 12t dt O el2 – 1 (e-) - 1) + 2 – 1 i - (e" - 1) j +k 12 O el2 12 O…

A:

Q: Describe the graph of the equation. r = 2 cos t i- 10 sin t j + k O An ellipse in the plane x = 1,…

A: Parametric plot÷

Q: Evaluate the limit using L'Hospital's rule 14* – 3" lim

A:

Q: 3. S- dx 1-sin'x

A:

Q: The graphs of f(x) and g(x) are shown. For what values of x does f(x) = g(x)? x = -2, x = 0, x = 3…

A: We have to choose correct option

Q: -2- At the point shown on the function above, which of the following is true? O f' > 0, ƒ'' > 0 Of'…

A: If the second derivative is positive then the graph of the function is concave up.

Q: Evaluate the limit using L'Hospital's rule 4* – 97 lim

A: Limit

Q: e cosx sin x dx 1-e2 cosx

A: Given problem:-