Y=t-2√√x + X

Q: Find the limit by interpreting the expression as an appropriate derivative. e2x 1 lim- = i x→0 X

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Q: Find when y = cos(sin 2x). ay dx dy dx

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Q: Evaluate 5² dV where E is the region below zx +2y + 4z = 8 in the first octant. Da B

A: Given problem:- Evaluate  ∫∫∫E  5x2dV where E is the region below x+2y+4z=8 in the first octant.

Q: A tank contains 420 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram…

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Q: If x is measured in degrees and f(x) = cosx, then d f(x) = − sinx

A: To write that it is true or not.

Q: 9. a. Explain why the Cartesian equation 2r-5y +3= = 2 does not describe the plane with normal…

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Q: Use the root test to determine whether the series converges or diverges. If the test is…

A: In this question, we need to determine whether the given series converges or diverges.

Q: Solve the following definite integral problems 1. Determine the area below f(x) = 8x - 2x² and above…

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Q: 2-¹ {; -} 18-7 s²+48 +9, In the process of calculating you obtain an equivalent expression given by:…

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Q: Find the average rate of change of g(x) = 5x³ + 4 from x = - 4 to x = 4.

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Q: ate the following integral using polar coordinates 17 'yx² (x² + y²j2dxdy

A: Above question is solved.

Q: Find the intervals where the function f(x) = 2cosx + 1/ sin2x, 0≤x≤ 2π is concave up.

A: Let's solve.

Q: Verify that the indicated function y = (x) is an explicit solution of the given first-order…

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Q: Find the integration by using substitution method. 2 dx x² - 6x + 10

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Q: Find f'(x). f(x) = = O V 10x - sin²(7x) 1 f'(x) = = 2√/10 - 14cos(7x) 1 f(x) 2√10x - sin² (7x) 10…

A: This question is related to differentiation, We will solve it using given information.

Q: If f(x) has an inverse function f-¹(z), could either the graph of for the graph of f be symmetric…

A: Given that fx has an inverse function f-1x. We have to check and explain if either the graph of f or…

Q: ³√x²e²²\ Which of the following is the most appropriate technique to use in evaluating O Integration…

A: The given integral is x2e-x.

Q: B/ Find the value of 1. tan+e O 1 2 dx 2. tante

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Q: The population of a town grows at a rate proportional to the population present at time t. The…

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Q: 1.) Sales of a particular product have been declining continuously at a rate of 8% each year. a.…

A: We need to find D.E. As per Bartleby's guidelines we can solve 1 question from multiple qn. Please…

Q: 79 J ·S= sen7⁹ (x) dx. When applying variable change u-cos(x) 39 ○ a) J = [ (1 − u²) 3⁰ du Ob) J=…

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Q: Find the derivative of f(x) = 2x3 + 12x² +18x + 9. f'(x) =

A: To Find : Derivative of f(x)=2x3+12x2+18x+9     Note that : Derivative of xn is nxn-1

Q: Exercise 2.5, Problem 26 a. Show that f has a removable discontinuity at x = 3. / f(x) = x² - 7x +…

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Q: What is the largest circular area that can be enclosed by 100 ft of fencing. (Non-anonymous question…

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

Q: 3) Find equations for the lines: a. The line through the point P(3,-4,-1) parallel to the vector…

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Q: Evaluate the integrals dx Så (4-x²)²

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Q: Let S = { 1 - (-1)" | n € N}. Determine inf S and sup S. Justify. n

A: We have to find the infimum  and  supremum  of the given function.

Q: In the process of calculating the inverse LaPlace of the function: F(s) = -21 - arctan (15) you…

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Q: Q3) Find the integration by using Partial fraction method Y x² + 2x + 1 (x² + 1)² dx

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Q: Determine whether the series converges. The series 8 k=1 13 15k

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Q: X xy of fr [²2/1/ ex None of the choices. The value of a. b. 0.07 c. 0.08 d. 0.05 0.06 e. dy dx is…

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Q: Find the directions of maximum and minimum change of fat the given point, and the values of the…

A: Let's find maximum and minimum rate of change.

Q: 3. log (x²+x)-log.(x-1)-2 А. 2 Oi J. оо о で В. 16 C..X D. - 16 -

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: dy Using logarithmic differentiation, find dx NOTE: Express your answer in terms of x only. dy dx =…

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Q: When does f(x) = ln(x + sin2x), 0 < x < 2π have a local minimum?

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Q: opulation P has doubled in 7 years, how long will it take to triple? (Round your answer to one…

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Q: The range R and the maximum height H of a projectile fired at an inclination 0 to the horizontal…

A: Note: Since, in the image of the question posted by the student, it is not clear how many place to…

Q: Determine whether the differential equation (7x+8) + (7y - 7)y' = 0 is exact. If it is exact, find…

A: To determine that the differential equation is exact or not.

Q: Let R be the region bounded by the parabola y = 4x² and the line y = x + 2. (a) Find the area of the…

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Q: Find the cumulative density function for the given probability density functio k(x) = 1.4 e 1.4x,…

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Q: Evaluate [(cos² 0 + 2 csc² 0 + sin²0) do. (a) 0 + 2 cot 0 +C (b) 0 2 cot 0 + C - (c) sin²0 + 2 cot 0…

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Q: Show that the solution y(t) of the initial value problem has the Laplace Transform y" + 2y' - 3y = 6…

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Q: Evaluate exactly lim(1 + sinx)2cot: x→0

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Q: 4) Find equations for the planes: a. The plane through P, (0, 2,-1) normal to n=3i-2j-k

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Q: -1₁ - S. -3√ 42² + +81(1+z)² dy .dz y = Z =

A: The answer is given below:

Q: Find the integration by applying (by part method) f Sin-¹y dy

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Q: x²-3x - 10 f(x) = x+6 [-2,5] Yes, Rolle's Theorem can be applied. No, because f is not continuous on…

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Q: Find the directions of maximum and minimum change of fat the given point, and the values of the…

A: Given:      fx,y=9y2e6x The gradient of a function z=Fx,y is denoted by ∇Fx,y The direction of the…

Q: A dart is thrown at a number line in such a way that it always lands in the interval [0,10]. Let x…

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Q: 6t²+t-5 9. lim t-∞ 9-2t²

A: lim  (6t2 + t -5)/(9-2t2 ) t --&gt;-∞ here question is of limit  and here we have to divide t2 by…