he transformation from Cartesian to plane coordinates in x-direction is given by x=rsine x=rcos20 x=rcose x=rsin28

Q: Find a rule for the derivative of the product of four functions f,g,h, and k. Use your result from…

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Q: 5. Solve d²y dy dx² dx +2 + 5y = sin 2x, given that y(0)=3, y'(0)=0.

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Q: True or False: We have Select one: True False 2 1² x²dx > 2 Si 1 x³ dx 3

A: Given ∫12x2dx>∫12x3dxx3312>x4412233-133>244-14483-13>164-1473>154Multiply 12 on both…

Q: Numerically estimate the slope of the line tangent to the graph of the function f at the given input…

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Q: The intervals on which f(x) = x² In x is increasing and decreasing, and the intervals of concavity…

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Q: Graph the function. n(x) = x -3 for-4<x<-2 for -2<x<4 -x² +16 for x ≥4

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Q: Graph all vertical and horizontal asymptotes of the rational function. 4x-11 2x+9

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Q: Consider the following. 2(x-8)² + (y - 6)² + (z − 5)² = 10, (9, 8, 7) (a) Find an equation of the…

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Q: Find sin(2x), cos(2x), and tan(2x) from the given information. csc(x) = 4, tan(x) < 0 sin (2x) =…

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Q: Let C be the curve y = 12 11 10 9 8 6 5 4 15 2 4 1 + for 0.6 ≤ x ≤ 3.7. 3x 25 Find the arc length of…

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Q: can you please write it clearly for better un

A: see below the answer and calculation

Q: Let C be the curve y = 12 11 10 9 8 7 6 5 4 15 x³ 1 + 4 3x 25 Find the arc length of C shown above.…

A: Use arc length

Q: Evaluate the following improper integral if it is convergent. S 13 -dx x In x Select the correct…

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Q: * The differential equation 2ydx-(3y-2x)dy=0 is Exact homogenous and linear Exact and linear but not…

A: The answer is given below:

Q: Numerically estimate the slope of the line tangent to the graph of the function f at the given input…

A: we can complete the table.

Q: The intervals on which f(x) = x² ln x is increasing and decreasing, and the intervals of concavity…

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Q: use a graphing utility to graph f(x)= -0.2x^3 - 0.5x^2 + 4x -4 on the interval [-6,4] and…

A: The given function fx=-0.2x3-0.5x2+4x-4 on the interval -6,4

Q: The value of the definite integral is Select one: 0 0 O 2/11 O-1/11 O none of the others O 1/11…

A: We have to solve above integral

Q: can you please write it clearly for a better understanding

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Q: Give a possible formula for the function below. Let A = (1, 21) and B = (2, 147). Use the general…

A: Given problem:- Give a possible formula for the function below. Let A = (1, 21) and B = (2, 147).…

Q: : Use the chain rule to find the derivative of w= x² + y² with dw with x = cost + sint, y = cost-sin…

A: This question is based on chain rule differentiation.

Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = xy² + 9, D = {(x, y) | x ≥…

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Q: Let à = i +43 and b - 37 - 7j. Find a . b

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Q: The intervals on which f(x) = x² lnx is increasing and decreasing, and the intervals of concavity…

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Q: The derivative of a^u with respect to x is

A: Aim:- To calculate : ddx(au)

Q: x(t) Find a plane containing the point (-4,3,-8) and the line y(t) z(t) = 8 - 3t 7 + 4t -8+ t

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Q: The value of the definite integral 3 [² (3x² S is (3x² - 2x + 4)dx

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Q: Evaluate the improper integral or state that it diverges. ∞0 S 125 dx 3 Select the correct choice…

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Q: Question 10 Evaluate the following expressions. sin (tan-¹(√3)) cos (tan-¹(1))

A: By triangle property

Q: A) Verify that y = C₁е¯x + c₂e5x is a solution of the DE: y" - 4y' - 5y = 0. B) Find a solution of…

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Q: then find f(x). | f(x)dx = = ln([x]) In(x) - sec(x) - 4e + 2 -x + 6x + C

A: The integration of f(x) equal to the;  ln(|x|)-sec(x)/3 -4ex/4+x2/2 +6x +C.

Q: In the find and prove of lim”→0 (x³), how and what should be defined in terms of ? A. 8 = min {1, §}…

A: This question is related to Limits, we will solve it using given information.

Q: bounded by the curve. Find the area y=2x+₁²₁ y=10x-x²

A: Given:  the curve is y=2x+12                               y=10x-x2

Q: The derivative of a^u with respect to x is a ln a du/dx (a^u) * du/dx ln a * du/dx (a^u) * ln a *…

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Q: Find the radius of convergence for: 3 (n!) ³ (3n)! n=1 xn

A: Recall that the radius of convergence for a series ∑n=1∞anxn is R=limn→∞anan+1

Q: Write an equation of the line that passes through (2.5, 1.6) and is perpendicular to the line…

A: Aim: To find equation of line passing through the point (2.5,1.6) and perpendicular to the line…

Q: can you please write it clearly for better un

A: To convert the polar coordinate 5, π4 to Cartesian coordinates.

Q: S cos 2x dx COSX

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Q: If y, and Y2 are linearly independent solutions of y" + 3y + (5 + t)y = 0 and if W(y₁, y2)(1) = 3,…

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Q: The Maclaurin series of the function f(x) = 2x² sin(9x) can be written as f(x) = Σcna" 71=0 where a…

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Q: Let a = 5j + k and b - 27 + 3 + 2k. Find - 3ā – 36.

A: We can find the given vectors.

Q: se series to evaluate the limit. 2 lim h→0 (sin h)/h- cos h h²

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Q: Evaluate 4 2 4 X 13.402 -13.402 13.042 √x + 3 3 X 4 - 4 + 4 + 1 + x)\dx = None of them -13.420…

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Q: function. f(x) = 2x-3 Start by drawing the vertical and horizontal asymptotes. Then plot two points…

A: We have to draw the graph

Q: 25 5.²5 4 Incx √x dx

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Q: The definite integral is equal to Select one: lò xác thỉ xác Of xdx + ² xdx Of xdx + xdx Of xdx -f²…

A: We have to find correct option of given integration by dividing limits.

Q: Find the sum of the series or show that it diverge 4 (a) Σn=1(3+2 + 8n-2

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Q: The temperature of a patient t hours after taking a fever reducing medicine is T(t) = 98 + 8/√t…

A: Here i have find the answer upto 4 decimal place.

Q: Two functions fand g are defined in the figure below. (a) ∞ Domain of f (b) Range of f 7 9 Domain of…

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Q: Find the value of ff xye**y dxdy (solve) (yeye)(xex - e*) Option 2 O yev (xe* -ex) Option 1 (yeyev)…

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