Verify that the hypotheses of Rolle's Theorem are satisfied for f(x) = x² - 8x + 12 on the interval [2, 6], and find the va this interval that satisfies the conclusion of the theorem.

Q: Use the given information to find the left- and right- hand Riemann sums for the following function.…

A: given function

Q: Sketch the graph of the quadratic function. f(x) = x² + 4x + 4 O S No Solution Help -10 9 8 7 6 5 4…

A: To sketch the graph of the following quadratic function.To indicate the coordinates of the vertex,…

Q: The graph of f(x) is shown (see figure). 6x x² + 1 f(x) (a) Find the following limits. lim f(x)= x →…

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Q: Find f(x) if f"(x) = 24x²+2x+8, f(0) = 5, f'(1) = -2.

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Q: 2. Solve the DE 1. 2. (D-D³-9D²-11D-4)y=0 (D-4D³ +8D²-8D+4)y=0

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Evaluate the integral: /9 - x² = dx (A) Which trig substitution is correct for this integral? 0x = 9…

A: Given indefinite integral is

Q: Kevin needs to find the length of the arc of the given curve. He is struggling. Please help him by…

A: given curve

Q: Evaluate u³(²-1)² du in terms of u by expanding the integrand. [/u³(²-1)² du = -/( 11 + C 1) du

A: To evaluate  in terms of  by expanding the integrand.

Q: A box is to be made out of a piece of cardboard 6 meters by 16 meters. Squares of equal size will be…

A: A box is to be made out of a piece of cardbord  meters by  meters. Squares of equal size will be cut…

Q: Question 5 (a) Determine the partial derivatives of the following functions with respect to each of…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 17-44. Indefinite integrals Use a change of variables or Table 5.6 to evaluate the following…

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Q: Evaluate the following integral. Š 12x - 61 dx

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Q: Consider the point whose Cartesian coordinates are (-1, –1,1) What are its cylindrical coordinates?…

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Q: Verify that the general solution satisfies the differential equation. Then find the particular…

A: Given general solution is .......(1)

Q: Compute the line integral f(x² + y)ds, where C is the arc of the circle x² + y² = 16 In the second…

A: To find The line integral, where C is the arc of the circle

Q: Reverse the ร fit 4 O √5x sle should order dy be of integration 18 doc dy for

A: To reverse the order of the following integration.

Q: 1. The value of a parcel of land bought for speculation is increasing according to the formula V=2…

A: The value of a parcel of land bought for speculation is increasing according to the formula V =…

Q: y = tan x S 2 1 1+t³ dt

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Q: -2 -1 2+ 1 T 1 y=h(x) 2 True/False True or False: At every point where h'(c) is zero or does not…

A: To determine whether the following statement is true or false.At every point where  is zero or does…

Q: You cost out a New York steak dinner.  Your cost is $7.00 and you want to put this on the menu for a…

A: You cost out a New York steak dinner. Your cost is $7.00 and you want to put this on the menu for a…

Q: Using  the following 1 kilogram = 1000 grams  = 2.23 pounds  solve   9 kilograms = how many pounds?

A: Given 1 kilogram = 1000 grams  = 2.23 pounds.

Q: part b) why do you divide theta by 360?

A: Formula for area of sector of a circle is given by               Where

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Q: Problem #4: When a 5 kg mass is attached to a spring whose constant is 20 N/m, it comes to rest in…

A: We have to find the position of mass when t= and amplitude after a long time.

Q: what is the domain of tan(x-(pi/4))

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Q: 2. Determine whether each of the following matrices are in row-echelon form, Reduced row-echelon…

A: A matrix is row echelon matrix if (i) The first non zero element in each non zero row is unity which…

Q: Z 0.68 (0). -0.68 -19.00.00 Drag the surface to rotate 0.68 Drag the surface to rotate t 0.00 .68…

A: From this picture, we can easily get the required traces

Q: Öz Given z = sin(y) where a=t+u and y=t-u, find Ot What is the formula for ✓ Find Oz Ət dz Ot : 8z…

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Q: Use the Chain Rule to check that the derivative of d dx 5 2(4-x-)- = = 1 (ਜ) 5 d 2 dx 5 2(4 – x²)² d…

A: We have to find the derivative of the given function using chain rule.

Q: Evaluate F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

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Q: Find the exact area, in fractional form, under the curve y = 4x³ over the interval [0, 5].

A: we have given function

Q: view Policies Current Attempt in Progress Find the area between y = x + 14 and y = 4x + 1 between x…

A: Giveny = x + 14, y = 4x + 1 and x = 0, x = 2

Q: Find the linear approximation for y=sin x at x = 0, and use it to approximate sin(0.3)

A: since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: Find the equation of the conic that satisfies the given conditions and graph the equation.…

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Q: ²6² F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify…

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Q: Use the Root Test to determine whether the series convergent or divergent. 5n 2n Σ (-20) ³ n+ 1 n =…

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Q: Use the reference angle to find the exact value of the following expression. sin 585°. (Simplify the…

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Q: Ise Newton's method to obtain the third approximation, X₂, of the positive fourth ro pproximation of…

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Q: A swimming pool has a depth of 5 ft at the shallow end and 10 ft at the deep end. The bottom of the…

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Q: Use Newton's method to estimate the two zeros of the function f(x)=x-x-2. Start with x= -1 for the…

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Q: (a) Use the figure to find the [ f(x)dx. -3 value of VA f(x) dx? L²₁ f(x) dx = = -10 (b) If the area…

A: Question No. part (b):If the area of the shaded is , then to find .

Q: (b) O Σ -1/2-²0 6 n=1 Sn Sn 10 4 n Sn 7.8749 2 4 5 n 6 X .... 6 8 7.8750 ... 8 10 10 10 X Sn Sn 3-…

A: Given series

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A: given the area of the region. We need to find the given integration value.

Q: The formula D = 25e-0.2h can be used to find the number of milligrams D of a certain drug that is in…

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Q: Test the series for convergence or divergence using the Alternating Series Test. 00 (−1)n + 1 Σ √n…

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Q: For which positive integers k is the following series convergent? (Enter your answer as an…

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Q: 2. Find the Wronskian of the following: b) (sin cos

A: We have to find the Wronskian for the given function.

Q: Apply the trigonometric substitution x = √3 sec(0). When determining the lower limit, you will have…

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Q: A 4.6 ft tall man is walking away from a 28 ft tall lamp post. If he is walking at a rate of 4 ft/s,…

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Q: Find the absolute maximum and absolute minimum values of the function f(x) = x + 1/ interval [0.2,…

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