Change the exponential statement to an equivalent statement involving a logarithm. ex = 10 The equivalent logarithmic statement is. (Type an equation.)

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Q: Compute the tangent plane to the function f(x, y) = x² + 2xy + y² at the point (2,1).

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Q: Find the volume of the largest rectangular box in the first octant with three faces in  the…

A: Find the volume of the largest rectangular box in the first octant with three faces in  the…

Q: Find the integral. √3x 31 Step 1 8x + 7 1-x² Split the integrand 8x + 7 V 1- x' | 31 J 8x + 7 dx…

A: Need to find the below integral∫8x1−x2dx

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Q: / I x+√√√x²=1 -1 I+ da

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Q: Find the indefinite integral. S t t4 + 36 dt

A: given integration

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Q: S Find the Maclaurin series of sin(t) t9 -dt.

A: Find the Maclaurin series of ∫0xsin⁡(t)t9dt

Q: If a rock is dropped from a height of 232 ft, its poistion t seconds after it is dropped until it…

A: Given :           The rock is dropped from a height of 232 ft.            s(t) =-16t2+232

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Q: The derivative of a power function: Note: the power rule works for any real n. )=x²! On short, (x")'…

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Q: Find fa, fy, fz. f(x, y, z) x²y 2z+1

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Q: dy du du' dx dy dx y = u53 and u = 5x4 - 2x² Find and

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Q: Let f(x) = 2 √-1-x+2 if x -2 Calculate the following limits. Enter "DNE" if the limit does not…

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Q: Find dy dx dy dx at (-8, 1) if xy = 40% x + 3 (Round your answer to four decimal places.)

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Q: y subject to the constraint x² + y² 4. Find the relative extrema of f (x, y) = 4x3 + y² subject to…

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Q: part I of the Fundamental Theorem of Calculus to find the derivative of L = 3x + 6x y = cos (u7) du.

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Q: I si sin³ (x) cos² (x) dx

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 5t²i - 5tj + 3t³k 2 (a) r(t) (b) r"(t)…

A: Note: As per the guidelines, I have solved three sub-parts. If you want the solution to the last…

Q: K Determine the following indefinite integral. dx S X√4-x16 S- dx 16 0- x√√4-x (Type an exact…

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Q: Find r(t) for the given conditions. r'(t) = 8e4ti +5etj, r(t) = 2(et)i+5e¹j 4t X r(0) = 2i

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Q: Find all the x-coordinates of points (x,y) on the curve y = (4x³-6x²+7x-1)(3x + 1)² where the…

A: y={(4x3+7x-1)(3x+1)2}

Q: A student takes the derivative of the function f(x) = as follows: d 1 d 2()-(x)--(~)--22 dx dx…

A: Given a solution of derivative  of a function.

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Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: 1 1 x2 − 6x + 10 dx

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Q: Find the differential y = In √3- = In (1 dy of the given function. (Use "dx" for dx.) - x² dy =

A: The Power Rule:The Chain Rule:And the common derivative:

Q: xy³ dx + (y− 1) ex dy _y=1 X = O =0

A: given differential equation

Q: dy dx x=a (4+h)¹ - 256 h The limit below represents a derivative lim h→0 . Find y = f(x) and a.

A: The derivative of a function f(x) at x=a is given byf′(a)=limh→0f(a+h)−f(a)h

Q: Complete the description of the piecewise function graphed below. -7 -6 -5 4 -3 H f(x) = -2 -1 1 if…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: The line LC²) = is (perpendicular) (neither) i (parallel) ii) (paralle 1) iii) (paNallel) i) to the…

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Q: Given h(w) Degree of h = 8 -0.016(4-2w)(-10-3w) (2w+7) answer the following questions: . The leading…

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Q: (x) = ₁² ² sin(t) -4x 1+t2 If f(x) = -dt, then f'(x) =

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Q: VOLUME: Sketch the region bounded by y = 4-x² and x- y = 2. SET UP THE INTEGRAL, BUT DO NOT SOLVE…

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Q: Given h(x) Degree of h = 4 3x + 6x + 24x answer the following questions: The leading coefficient of…

A: The x intercept of a function is the point where the graph crosses the x axis.The yintercept of a…

Q: For the given cost function C'(x) = 12100 +500x + x² find: a) The cost at the production level 1450…

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Q: Find the indefinite integral. (Use C for the constant of integration.) 9 Z₁ Z√ 492²-64 2 tan S 2 -1…

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Q: Find the derivative of the function below. Use lower case letters. p(y) =ay.eby dp = dy

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

Q: is given by the function s(t) = -16t² + 232. Round values below to 3 decimal places. How long does…

A: Given :           The rock is dropped from a height of 232 ft.            s(t) =-16t2+232

Q: The function s(t) describes the motion of a particle along a line. s(t) = 16tt² (a) Find the…

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Q: Differentiate. x + √x √x+7 )-\x( (√x+7)²

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Q: A 50 000L tank can be drained in 30 minutes. The volume of water remaining in the tank after t…

A: Given   V(t) = 50000(1-t/30)^2  ;0<=t<=30 To find the rate at which the water is flowing out…

Q: dy' dx (6.) (i + cos x ) = X = 0 y = 1 sinx (sinx tsinxcosx -y) Answer: C=1/12/2

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Q: The revenue function is given by R(x) = x · p(x) dollars where x is the number of units sold and…

A: The revenue function is given by  dollars where x is the number of unitssold and  is the unit price.…

Q: Consider the function f(x) this interval. = 1 on the interval [2, 11]. Find the average or mean…

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Q: Suppose R '(1) = 6. (a) If f(x) = R(4x), find f f' (1/1) 4 || (4). (b) If g(x) = R(x + 2), find g…

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Q: Consider the following. f(x) = (4x)² (a) Sketch a graph of the function f. 6 -8 -6 -4 -2 2 4 -2 2 N…

A: The given function

Q: nd [₁9(a) d g(x) dx = -10, evaluate the integral If g(1) = -4, g(5) = -4, and [₁²xg' xg'(x) dx.

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