On which interval is the function increasing? * 40- 20- 2. 20- -40- O (- 3, 3) O (3, 5) (- 5, - 3) O (+ 5, 5)

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = , (1, 7, 7) 10 z…

A: We have to find equation of tangent plane

Q: x² – 16 Evaluate lim x4 2- Vx O -32 None of these 1 O 32 O does not exist

A: Given  Lt   x²-16/(2- √x)        x->4

Q: Consider the function f(x) whose second derivative is f''(x)=2x+3sin(x). If f(0)=2 and f'(0)=4, what…

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Q: The sum of two positive numbers is 20. Find the product of the two numbers if the sum of their…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Fove that y = ln|| is a solution to 1+e-22 - xey-x² . Use the initial values x = 0 and y = 0.

A: Given query is to find the solution of the differential equation.

Q: Given f(a) = 1- 홀 (3 + 4a) + 용(3+ 4z)2 - 꿈 (3+ 42)3 then f'(x) = 27 (3 + 4x) 8. 흥(3+ 4z) + (3+ 4z)2…

A: topic - derivative of a function

Q: Suppose f'(x) = sin(2x²). d ; f(7æ) =| dr d de f(32®) = [

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Q: Find the equation of the tangent line and the normal line of the curves at given point 1. y = x V16…

A: Equation of tangent line Consider y=x16+x2slope of the tangent line is dydx  at…

Q: Consider the function y = 4ex + 7. What is the exact value of C in the interval [0, 5] such that…

A: We need to find value of C.

Q: Find the maximum value of the function f(x) = x³ -9x2 + 15x - 5. Answer: Find the value of x for…

A: In order to find the critical values we need to differentiate f(x) with respect x and then equate it…

Q: 1. The Fibonacci sequence is given by the recurrence relation a, = a,-1 + a,-2; a, = 0, a, =1. Write…

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Q: 1. write the slope-intercept forms of the equations of the lines through the given point (a) paralel…

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Q: A student throws a ball upward from a height of 48 feet, initially at 32 ft/sec. The function that…

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 4, (1, 2) Vf(1, 2) =

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Q: Let the region R be the area enclosed the function f(x) = x², the horizontal line 6, and the y-axis.…

A: Explained below

Q: der the following planes. 5x + 2y – z = 44 x – 4y + 2z = 0 (a) Find the angle between the two…

A: Angle between planes and line of intersection of planes

Q: Your professor said that this cannot be solved using Power or Logarithm Formula alone. Other formula…

A: The general form of integrand to apply power formula∫fxndx = fxn+1n+1 + CIn the given problem,…

Q: Which of the following is 2 equivalent to tan x + cot x where x = -? 2 sin 0 2 sin 0 2 Option 1…

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Q: A student throws a ball upward from a height of 48 feet, initially at 32 ft/sec. The function that…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Given f''(x)=9x+0 and f'(0)=−3 and f(0)=4.   Find f'(x)=     and find

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Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. y y= fix) 6.…

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Q: 9/ Evaluate (cos* 0 – sin* 0)de T/12

A: Note that: cos4θ-sin4θ=(cos2θ-sin2θ)(cos2θ+sin2θ)=(cos 2θ)(1)=cos 2θ

Q: Find an equation of the tangent line to the graph of f(x) = xe−x at its inflection point.

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Q: When an object is located a distance of x feet from the origin, a force of x2+3x  pounds is acting…

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Q: The number of bacteria in a culture is increasing according to the law of exponential growth. The…

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Q: Find the orthogonal trajectories of the given family of curves. Draw a few representative curves of…

A: For orthogonal trajectory we replace dy/dy by -dx/dy

Q: The sum of two numbers is 8. The product of the first number and the square of the second number is…

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Q: If the surface area of a cube is increased by 96%, by how much has the edge increased? 96% 92% O 40%…

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Q: At which points on the curve y = 1 +°40x³ – 3x³ does the tangent line have the largest slope? | (x,…

A: Maximize slope

Q: Find the general form of f if f'(x)= 9f(x). f(x) = ]

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Q: Question Use the First Derivative Test to find the location of all local extrema for the function…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = Y, (1, 8, 8) 10…

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Q: find the inverse laplace tramsform 3/(s-2)^2+4

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 3y2 + 2, (3, 5) Vf(3, 5) =

A: Given: fx,y=2x+3y2+2 ; Px,y=3,5   As we know that; The expression for the gradient vector.…

Q: Integrating Factor by Formulas: (4) (4xy + 3y² – x)dx + x(x + 2y)dy = 0 (5) y(x + y + 1)dx + x(x +…

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Q: At a point 160/3 feet from a building, and in a horizontal line with its base, the angle of…

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Q: fin the general solution of (x+2y-4)dx - (2x+5-y)dy=0

A: Please see the below picture for detailed solution.

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

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Q: dy J 1+y+1

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. x =…

A: Given problem:- Consider the solid obtained by rotating the region bounded by the given curves…

Q: 1. Solve the given the equation using the integrating factors found by inspection. ydx + (x + x³…

A: Given that ydx+x+x3y2dy=0Solution :ydx+x1+x2y2dy=0this diffrancial equation in the…

Q: 6.(Somewhat tricky) Use an appropriate substitution to solve: (a) dy y + x dx (b) (y³ + y?x) dx – x³…

A: To solve the following differential equation

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (2, –3)…

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Q: 12 dx Evaluate the integral: (9+3x)3 63 1. 36 1. 99 None of these 72

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Q: Solve eX = 6 for x. The solution is x2 (Round to four decimal places.)

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Q: %3D Find the maximum value of the function f(x) =x° - 9x2 + 15x - 5. Answer: Find the value of x for…

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Q: The following set of data represents the number of families (n) moving into a new town as a function…

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Q: Exact ODE y'=-4/x; y(2)=3

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² – 2xy + y²,…

A: Given problem:- Find an equation of the tangent plane to the surface at the given point. f(x, y) =…