2) Given: f(x) = x+sin(2x) over the interval (0,7) a) Use a sign analysis to find the relative extrema using both the first and second derivative tests.

Q: Compute f'(a) using f' (a) f(а + h) — f(a) = lim f(x) or f'(a) = lim f(a) for f(x) = 10x³, a = 2.…

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Q: lim(8x + 16) = 24 Use the epsilon-delta definition of limit to prove that æ→1

A: Let's find.

Q: Find the first and the second derivatives of the function. y%3D 6-x

A: The given function is: y=x6-x  =-xx-6  =-x-6+6x-6  =-1+6x-6  =-1-6x-6

Q: e2" (x + 1) cx – e(x4 – 1)dy = 0 d Hint: 4 (arctan x) = dx 1+x*

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Q: Find the area of this parallelogram. Be sure to include the correct unit in your answer. cm 8 cm 10…

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Q: Consider the following. (If an answer does not exist, enter DNE.) (x) = x6e=x (a) Find the…

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Q: TRUE OR FALSE. The curve defined by the polar equation r = 2 + 3 sin θ is symmetric with respect to…

A: To determine whether the given statement is true or false.

Q: cos (x) tan (x) dæ

A: I have stated the used formulas in the solution

Q: 24. f)dx + fx)dr =,

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

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Q: y" + 4y' = cos(t – 3) + 4t, y(3) = 0, y'(3) = 7

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Q: _14. Suppose that a function f: R² → R and its partial derivatives up to the third orders are…

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Q: 4. S Vä(x² + 2) dx 5. S(-3 Vã – 6x v7) dx 6. (9x*-6x²+7x²-5x+15 dx 3x

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Q: 17. (Vx-x)dx (1-x²) dr 18. 19 o. Sy² dy 20.

A: Given problems:-

Q: Given: dx x3 Using trigonometric substitution, solve for the integral form in terms of 0.

A: This question can be solved by taking x=3secθ

Q: 7 -4 Consider the surface x'z* + sin(y zª) + 9 = 0. Use implicit differentiation to find the…

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Q: 4. y²tan y

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Q: Given that cos(2x+y）=4xsiny, where 0≤y≤π, find the value of y and dy/dx when x=0

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Q: lim -1 x→0+

A: Separate the limit.

Q: Use the limit definition to calculate the derivative at x = a of the linear function f(x) = 31.…

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Q: 3) consider the regionnin the second quadrant betueer the circles x?+yZ=4andx2+y2=25, and above the…

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Q: x² –9 dx Given: r3

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Q: Find the total area enclosed between y = x and y = x over th- %3D interval [-1,6]. NOTE: Enter the…

A: Here, to find the area enclosed by y=x3 and y=x over the interval [-1,6].

Q: Given : S 6x³e**3 dx. Using integration by parts (S udv = uv – dv = 3g(x)dx find h(x) if ſ vdu =…

A: Let's find.

Q: Given x sin (yz) + y³ cos (xz) + z sin (xy) = v3. Find əx (a) implicit differentiation, (b) by…

A: a) Implicit differentiation: We will treat y as constant.…

Q: What change of variables is suggested by an integral containing * Vx² – 4? O a cosø O none of the…

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Q: Integration by Parts Example 4. Evaluate In x dv,

A: The given integral is: I=∫lnxdx   As we know that; ddxlnx=1x

Q: %3D Determine the speed along a parameterized path c(t) = (6 sin¬'(t), 3 tan¬(1)) at time t = 0…

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Q: 4. Suppose U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {3, 4, 5, 6, 7}, B = {all multiples of 3} and C =…

A: U=1,2,3,4,5,6,7,8,9A=3,4,5,6,7B=all multiples of 3C=all multiples of 2

Q: Consider the equation below. (If an answer does not exist, enter DNE.) (x) = xe8x (a) Find the…

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Q: If R is the region enclosed by x-axis, y = -3x and x = -2, then evaluate the following double…

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Q: (xcosx + sinx) dx + -sinx + 6 )dy y = 0;x=0;y=1 |

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Q: 4) Equation: 4x +9y² = 1 1 Given that dy/ dt =8, find dx / dt when (x,y)= 3 9

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Q: x³ + 6x? + x+2 How many linear and repeated factors are in the denominator of x³ +1

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Q: Evaluate the integral 20 2) dr by making the substitution u 2. NOTE: Your answer should be in terms…

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Q: What are the polar coordinates of the point Q shown below? 1 2 3 4 5

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Q: What will you factor out from the integrand of ] csc°(3x)dx so that you can transform it to its…

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Q: u+ 2v = 1+ vw; w, and vw. w

A: To find the partial derivatives for given function.

Q: 5. [ +4x+3 x4 –5x2+4

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Q: ナ+sy'+by =4et も

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Q: II. Matching Type: Match the definite integral in column A with its value in column B. Letters only.…

A: 11. ∫022x-3dx12. ∫-11x3+2xdx13. ∫03x2-2dx

Q: The loop of the following limacon is produced for which interval of the angle theta?

A: Given:       r=2+4sinθ The first step is to find the angular displacement of the inner loop. To do…

Q: x arcsec x dx ? xdx A. x Arcsec x - 25- ... B. ** Arcsec x -- V-1 xdx xdx C. x Arcsec x + 25- xdx D.…

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Q: Convert x = 19 to an equation in polar coordinates in terms of r and 0. (Use symbolic notation and…

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Q: x² - dx ? Using trigonometric substitution, what is x3

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Q: What are the polar coordinates of the point P shown below? 2 3 4

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

Q: Vx In 2x dx=u v- v-fvdu Using Integration By Parts, Find Uv- du O 3 xVx In 23 2 12x- dx | O 2 Xx In…

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Q: Evaluate the definite integral: 4 dx 0 x2+16

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Q: all

A: We have to find the following conditions according to the given graph of the function

Q: Using Integration By Parts, x sec - x tan x dx = %3D

A: Use integration by parts.