For z>0, y > 0, z, y € R, find the value of (log, y) (log, a)

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A: The given integral is

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A: General equation of sphere -(x-h)2 + (y-k)2 + (z-l)2 = R2where,(h,k,l)= centre R = radius

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Q: Write an equation for a sphere centered at the point (8,4,-3) with radius 7.

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Q: = z. Evaluate the triple integral|]] (r g(x, y, z) dV over solid, B = {(x, y, z) | x² + y² ≤ 25, x ≥…

A: Given that To find  where

Q: Question Find the volume of the solid obtained by rotating the region bounded by y=3x2, x=1, x=3,…

A: The objective of this question is to find the volume of the solid obtained by rotating the region…

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A: Here we have to set up integral which gives the arc length of the function.I have appended the…

Q: Evaluate the definite integral. 6.² sin (4t)dt

A: Let assume,

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A: Given in Mendel's genetic experiments many characteristics( height, flower position, seed color ) of…

Q: Suppose F(t) has the derivative f(t) shown below, and F(0) = 6. Find values for F(1) and F(7) 2 3 2…

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Q: Find the linearization of the function f(x) = √10 – x² at a = = 1 O L(x) = =¹²(x − 1) + 3

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Q: Find the limits, if they exist, or type DNE for any which do not exist. 1) Along the x-axis: 2)…

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Q: Find all horizontal asymptotes of the following function. f(x) = 2(3x - 10) 3(52+9)

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Q: If f(x) = cos x, then f'() = A. B. - C. - C. D. √3

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Q: Given T(t) is the temperature inside a math classroom at time t. The first derivative is given by…

A: Given: To Find: To find the time(s) during the interval  where  has a local maximum.

Q: Let f³ f(x)dx = 12, f³² ƒ(x)dx = 3, få ƒ(x)dx = 4 ƒ² (2ƒ(x) — 1)dx Find

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Q: 21) Evaluate the limit, if it exists. If it does not exist enter DNE. x² - 6x + 5 lim- x→5 x - 5

A: The given function is .The aim is to find the value of the limit.

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 8-x², as shown…

A: The given parabola is .The aim is to find the largest area the rectangle.

Q: C(x) 1 Suppose that the total cost (in dollars) for a product is given by 1400 + 190 ln(2x + 1)…

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Q: Determine the compromised areas between the given curves and lines. x = lny, y = 1, y = 4

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Q: Compute the given indefinite integral. [(-3 3 + 5z + cos (32)) dz =

A: Consider the integral

Q: Assume f(3) = 0, f'(3) = 6, g(3) = 1, and g'(3) = 3 f(x) g(x)* Find h'(3) given h(x) = A. -2 B. 2/2…

A: Given,

Q: Question 4.2. In each case let R be the region under f over the given interval and let S be the…

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Q: Let f be the function defined by f(x) = e cos(x) (a) Find the average rate of change on the interval…

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Q: A coin is tossed 9 times. What is the probability of getting heads exactly one time? Round your…

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Q: (3) J -x² + 4x 2 x³ + 4x² + 4x + 3 dx

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Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A: Dr. Jones suggests fences described by The graph of the curves of the shape of the fence is:

Q: x4 x²+x-6 S dx

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Q: f(x) = Cos (3x) as a 6th degree polynomial centered at x = 0. Hint use the following: P₂(x) = ƒ(0) +…

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Q: Complete the square and find the indefinite integral. (Remember the constant of integration.) x²…

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Q: etermine whether the matrix A [ 0 4 ] [-4 0 ] is diagonalizable .

A: A=[0 -4      -4 0]

Q: Use the disk method or the shell method to find the volume of the solid generated by revolving the…

A: The region is bounded by the curves

Q: Find the interval of convergence for the given power series.∞∑n=1n4(x+3)n(10n)(n143)The series is…

A: The objective of this question is to find the interval of convergence for the given power series.…

Q: Given the point (1-2) is on the graph of y=f(x), determine what those coordinates would be on the…

A: we need to find the image of the given point

Q: [s sin x cos x esin²x+dx = A B C D - sin x cos x esin²x+ esin²+ + C 1/2 (sin ²x + 7) + C e -…

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Q: An angle is between 90° and 180°. You also know that csc = 1.5. Calculate all the other…

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Q: If the point (-1, -2) is on the graph of y = f(x) , what must the point be on the graph of y = f…

A: We have given a point on function f. Now the function is transformed into y = f (x-2) +5.We have to…

Q: The events E and F are mutually exclusive if their intersection is empty. Select one: O True O False

A: Given that E and F are mutulayy exclusive

Q: Problem (2) Consider the region in the first quadrant under the curve y = 1 − 4x²,0 ≤ x ≤ 0.5. Use…

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Q: Given the position function s = 12 +9t-5, what is the instantaneous rate of change at t = 3? A. 2t…

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Q: X f'(x) 0 4 1 3.5 2 2 3 0.8 4 1.7 5 5.8 6 7 4. The function f satisfies f(0) = 20. The first…

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Q: If f(x) = 1/2 · cos x, then f'(x) = I A B C D sin a x² -1-x² sin x x² cosx-xsin x x² cos x+xsin a x²

A: As we can see f(x) is product of two functions i.e 1/x and cosx.We use the formula for derivative of…

Q: [1 0 1] Find the inverse of the matrix C = 0 1 1 using 2 1 4 cofactors. Show all your work.

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Q: A given poll states "61% of high school graduates felt they were prepared for college." If there is…

A: The objective of this question is to calculate the 95% confidence interval for the given statistic,…

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Q: Which step is part of finding the derivative of the function below? The correct choice may not be in…

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