Find the gradient of the function at the given point. Function g(x, y) = ye-x Vg(0, 9) = Point (0,9) Find the maximum value of the directional derivative at the given point.

Q: Find a unit normal vector to the surface at the given point. [Hint: normalize the gradient vector…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: . Find the open interval(s) on which the function is increasing and decreasing.

A: Given :f(x)=9x3-11x

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: The number of traffic accidents per year in a city of population p is predicted to be T 0.002p ³/2.…

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Q: s help A

A: calculus

Q: Consider the following second-order differential equation. 2y" + y = 0 Find all the roots of the…

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Q: 1. DIFFERENTIAL EQUATION (2y³ + 4) dx = (6-2xy²) dy

A: Note :- These are multuple questions and according to our comapny guideline we can do maximum 1…

Q: 9) 1 What value(s) of x makes + ed 0.91/14 4|33|4 b. 0, X x+4 = 2 true? C. d. 2√√3 3 3

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Q: 3) y" + 4y' + 4y = 0.

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Q: Find c> 0 such that the area of the region enclosed by the parabolas y = x² - c² and y = 2²-² is…

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Q: Find the inverse function (if it exists) of f(x) = ln (1-2x). If the function is not invertible,…

A: NOTE: Refresh your page if you can't see any equations. . to find an inverse function, interchange…

Q: QUESTION 1 P 0 0 9 0 00r Show that 0 Hence, determine the inverse of the following matrices: 100 i.…

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Q: 9-x2 x dx

A: ∫9-x2x2dx=∫cot2udu=∫ -1+csc2udu=-∫ 1du+∫csc2udu=-u-cotuSubstitute back…

Q: the origin 2 2 S (1-10²1) ² dx -1 2

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Q: Select all that apply: f(x) is not continuous at x = 3 because limf(x) ‡ƒ(3). Of(x) is continuous at…

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Q: 3 g-¹(x) = = (Write your inverse function in terms of the independent variable x.) Find the inverse…

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Q: gas station stands at the intersection of a north-south and east-west road. A police car is…

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Q: Find the limit of s(n) as n → ∞0. ( s(n) = 4 n n(n + 1)(2n + 1) 8

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Q: Find the sum of the areas of the shaded rectangles under the graph. Round to two decimal places.…

A: topic- Area of shaded region Area of rectangle =Length*width

Q: 1 if x > 0 x²-1 if x ≤0 g(x)=x-1

A: Given the function, gx=1x-1if x>0x2-1if x≤0

Q: Find equations of the spheres with center (2, -3, 5) that touch the following planes. (a) xy-plane…

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: Analyze the following graph of f'(x). Select all of the intervals over which f(x) is concave down.…

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Q: ∞ Determine whether the series (-1)-In -1/3 is absolutely convergent, conditionally conver- n=1

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Q: Determine csc(x) + cot (x) if tan x + sec(x) = 22/7. 27/12; 29/15; 24/18; 23/11

A: We can answer the question by finding the correct option as below.

Q: For Luce landscaping, the total revenue and the total cost of yard maintenance of x homes are given…

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Q: Find the area between the curves. x = -5, x=2, y = 2x² +5, y = 0 The area between the curves is…

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Q: Find the intervals where the curve is increasing and where it is decreasing. Also, find all z values…

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Q: Integrate f Osin-15x+C ○ -sin-¹5x + C 1 dx 1-25x2 - 5 H|K sin ¹5x + C cos ¹5x + C

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Q: 1. (Use a calculator) Write down the equation used to evaluate the following expressions, and then…

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Q: 14) At what point on the graph of f(x) = instantaneous rate of change? a. x8, x = 2 b. x = 4…

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Q: 1) y" - 36y = 0.

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Q: Use Properties of Exponents and Properties of Logarithms to simplify and the following expression…

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Q: 1 Q BAS 6 2 [//dx Which of the following is the integrand in the definite integral above? Select the…

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Q: Find the real roots of the equation B 244

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = X, (1, 7, 7) 10 5…

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Q: ∞ Determine whether the series (-1)"- n gent, or divergent. n=1 is absolutely convergent,…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

A: here is the solution:

Q: | (8z + 4z³ - 6z²) dz? O 16z²+z4-2z³ + C O4z²+z4-22³ + C 16z²+z4+ 2z³ + C O 42² +224 + 2z³ + C

A: Solution: ∫8z+4z3-6z2dzApply the sum rule=∫8zdz +∫4z3dz -∫6z2dz

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: ƒx(2x−1) dx 2 √x³√x²+4 dx

A: for (1),     ∫ x2x-17dx=∫ 128x8-448x7+672x6-560x5+280x4-84x3+14x2-xdx=∫ 128x8dx-∫ 448x7dx+∫…

Q: Simplify to an expression involving a single trigonometric function with no fractions. cos(-x)…

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Q: 1) State the vertical asymptotes of f(x)= a. x=6₂x=-2 b. x=6, x=2 1 x² - 4x-12 c. d. x=-6, x=-2…

A: Given:         fx=1x2-4x-12 Vertical Asymptote:     For rational functions,the vertical asymptotes…

Q: Sketch the region R of integration and switch the order of integration. 81-x2 LV²²- -10 O -10 f(x,…

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Q: Please

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Q: Find the area of the region bounded by the graphs of the given equations. y = 6x-x², y = - 2x The…

A: The given curves are: y=6x-x2, y=-2x   Now find the point of intersection between the given curves.…

Q: 3. [x²cos2x dx

A: The given integral, ∫x2cos2x dx Note:    Multiple questions are given, we are answer only one…

Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

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Q: An exponential function f(x) = ab passes through the points (0, 3) and (3, 375). What are the values…

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Q: Evaluate the integral. X √ ² ₁x + (x + 16y) dy

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