d dy (^-1^²)

Q: 1. If f(x, y) = 3x + 7y2 and u = 3i+ 4j, find the directional derivative at point (1,1).

A: f(x,y)=3x+7y2u=3i+4jPoint (1,1)Find the directonal derivative.

Q: Find the centroid of the region bounded by y = 3 sin x, y = 0, x = 0, and x = π. (Hint: Sketch the…

A: y = 3sinx,y=0 0xπ

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the 4 region bounded on…

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Q: The atmospheric pressure on an object decreases as altitude increases. If a is the height (in km)…

A: The atmospheric pressure on an object decreases as altitude increases. If a is the height (in km)…

Q: 5. 13: I can estimate the value of a definite integral using a table, Riemann sum, or technology. A…

A: I have appended the formula used in the solution procedure

Q: Consider the function f(x) = 3x² - 10x +9, 0≤x≤7.

A: f(x)=3x2−10x+9,0≤x≤7

Q: Differentiate In [(3x4 + 2x³ − 7x)(4x² +9)]

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Q: Find two positive integers such that their sum is 28, and (a) maximize and (b) minimize the sum of…

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Q: The following limit results in 0 when you first try to plug in the limit value. 0 Complete the steps…

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Q: Find the difference quotient of f; that is find f(x+h)-f(x) h The difference quotient of f;…

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Q: 2.5 10- 0- -10- PIC COLLAGE

A: WE are given images of graph of functions We have to identify the graph of logarithmic function.A…

Q: A company selling widgets has found that the number of items sold a depends upon the price p at…

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Q: Find the derivative a. ((3x2-pix)4)/6 b. 3square root x2 - 1/square root x3

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Q: Find the open interval(s) where the function is changing as requested. Increasing; y=√√x² + 10

A: y=x2+10

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: Let g(x)=2x²-1. (a) Find the average rate of change from - 1 to 8. (b) Find an equation of the…

A: g(x)=2x2−1

Q: Evaluate the following integral. 1/5 1.1 0 x tan¹ (5x)dx

A: To evaluate the following integral.

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A: In the question we have to find the number of units which will provide maximum profit.

Q: Derivative Rules: 1. Power Rule: d dx Special Case of this: 4. Quotient Rule: -(x²): = nữ Given the…

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Q: Practice 2: If y =cos'' x prove Hint: use the equivalent statement differentiation. dx 1 VI-X y=cos…

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Q: 7. Differentiate the following function to review unit two. a. b. C. y' = y' = y = t² + 1 4 - 3t² +…

A: a) y=(t2 + 1 )/(t4-3t2 +2)b)F(y)=(1/y2 - 7/y4 )(y+ 5y3)c)y=sec(theta)tan(theta)According to Bartley…

Q: 4. Students were asked to formulate the system of equations needed to solve the following problem:…

A: Let x = amount of beansLet y= amount of bread

Q: Practice 1: f(x)=√x X+1 fferentiate and simplify your answer:

A: The given function is

Q: Find the volume of the solid obtained by rotating the region bounded by y = 8x², z = 1, and y = 0,…

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Q: (a) Find parametric equations for the line segment that joins the point P(-1,-4,-3) to the point Q…

A: Question no. 1(a):To find the parametric equations for the line segment that joins the point .Note:…

Q: 3 4. y sin³ 4x cos 4x =

A: The given function To find:-The integral in terms of sine function

Q: Identify at least one pair of an inner function and an cuter function for each of the following…

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Q: For y = f(x) = 7x², find f(x₁+AX)-f(x₁) Ax || f(x₁ +Ax) -f(x₁) Ax given x₁ = 5 and Ax=2.

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Q: Find the exact length of the curve. x = 9 cos(t) - cos(9t), y = 9 sin(t)- sin(9t), 0 stST

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Q: Find the directional derivative off at the given point in the direction indicated by the angle 8.…

A: Consider the function

Q: Consider the graph of y = y 3 2 1 -1 -2 -3 f(t) dt, where f is a piecewise constant function. 2 3…

A: The graph of a piecewise function is given as,

Q: SS (27y²-4x) dA (27y² - 4x) dA R: 0≤x≤3, 0≤y≤2 R

A: ∬R(27y2−4x)dAR:0≤x≤3,0≤y≤2

Q: log(x2+x+ ex cos(x)²) log(log(log(x)))

A:

Q: 2. Students were asked to formulate the system of equations needed to solve the following problem:…

A: 2.Bob and June have $100,000 that they wish to invest in three different stock funds. Fund A has a…

Q: Find exactly the relative extrema of the function (a) Find X-coordinate of relative minimum point. X…

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Q: Suppose R is the shaded region in the figure. As an iterated integral in polar coordinates, A = B =…

A: The figure

Q: EXAMPLE 5 If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional…

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Q: Use the first derivative test to locate the relative extrema of the function in the given domain,…

A: The given function is

Q: Find f(x) if y = f(x) satisfies dy dx e¯½ f sin x and ƒ (7) = ²/

A: Given the experience  and y=f(x) we have to find the solution f(x) by the condition

Q: You are constructing a cardboard box from a piece of cardboard with the dimensions 2 m by 4 m. You…

A: We are given a cardboard with dimensions .

Q: y = f(g(x)) 1 x + 19 y= U = u = g(x) y = f(u) y = u ¹/2

A: y=f(g(x))u=g(x)y=f(u)y=1x+19u=◻y=u−1/2

Q: Find the tangent line approximation T to the graph of f at the given point. Then complete the table.…

A: Consider the function

Q: ind the limit if it exists. lim (12x+11) elect the correct choice below and, if necessary, fill in…

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Q: Consider the function f(x) 2x²10x + 11, 0 ≤ x ≤ 7. The absolute maximum of f(x) (on the given…

A: Given that the function, we have to find the absolute maximum and absolute minimum value

Q: Find all the critical numbers of the function. 2 f(x) = x³ + x²-21x+2 OA. 3 OB. -3, -3, 7/2 OC. -…

A: In this question, we will find the critical point.

Q: find the derivative a. f(x)=[ln(5x^2+9)]^3 b.f(x)=ln(5x^2+9)^3

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Q: A cable that weighs 4 lb/ft is used to lift 600 lb of coal up a mine shaft 400 ft deep. Find the…

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Q: 10 -9 he function f (x) -8 -7 -6 -5 5 4 3 92 -4 -3 -2 -1 1 -1 -2 -3- -4 -5+ 2 3 O 5 67 Determine the…

A: Infinite Discontinuity: A function has an infinite discontinuity at a point if the function…

Q: sider the ction or a pen to enclose an rea. You have 400 ft of fencing to make a pen for hogs. If…

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Q: Graph the function hoo-x-30 0x30 30x50 0.5x-65 i x>50 Choose the correct graph below OA 1530456075…

A: