Find the gradient of the function at the given point. Function f(x, y) = x² Point (4,4) Vf(4,4) = x² + 2xy Find the maximum value of the directional derivative at the given point.

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: Use the gradient to find the directional derivative of the function at P in the direction of v. h(x,…

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Q: x, evaluate each expression.

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In√√x² + y2, (3,…

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Q: If f(0) = 1 and lim (a) -1 sec xf (t)-f(x) sect t-1 (b) 0 2 =sec x. The value of (c) 1 f(0) f'(0)' ,…

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Q: A x Given that cosa= and 0 <a<, determine the exact value of cos 3 A cos = (Simplify your answer,…

A: All trigonometry ratio are positive in first quadrant .

Q: Evaluate the following limit or explain why it does not exist. 6 X lim (1+7x) X-0 Select the correct…

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Q: rary S ebook chedule esources ptions ick Guide Cation Tools cloudy Find the measure of the angle 0.…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Consider the following. u = −7i - 2j - 4k, V = 4j + 4k (a) Find the projection of u onto v.

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Q: Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100 mg…

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Q: Verify the identity. sin(x) + cos(x) = sin(x) cos(x) sec(x) + csc(x) sin(x) + cos(x) sec(x) + csc(x)…

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Q: Find the exact value of the following expression. sin (sin ) Select the correct choice below and, if…

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Q: Solve the problem. Find the amount of interest earned on the following deposit: $1,000 at 4%…

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Q: Use the properties of the derivative to find the following. r(t) = ti + 5tj + t²k, u(t) = 4ti + t²j…

A: This question is based on dot product of two vector. (a i + b j).(c i + d j) = ac + bd

Q: 3. [x²cos2x dx

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

Q: 5. [tan³x sec³x dx

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Q: TryMaryviar yıvıar Question 9 of 10 Find the equations of the tangent lines to the graph of y=x2+6…

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Q: Evaluate the following integral: dx -27 x2/3

A: Solve the following

Q: 1) If the sum of the squares of five numbers is 165 and their variance is 8. What is the mean of…

A: Since multiple questions are asked, I am answering first question

Q: Find the absolute maximum and minimum values of the following function on the given region R.…

A: To find the absolute maximum and minimum.

Q: Determine the remaining sides and angles of the triangle ABC. What is the measure of angle B? 0° B…

A: This is a problem related to sine cosine rule of trigonometry. Please follow the procedure given…

Q: Given f(6)=3, f′(6)=11, g(6)=−1, and g′(6)=7, find the values of the following (a) (fg)′(6)= (b)…

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Q: A local club is arranging a charter flight to Hawaii. The cost of the trip is $543 each for 83…

A: We need to find no. of passengers and max. revenue.

Q: Evaluate the following integral: Stan x sec³ x dx

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Q: Find a set of parametric equations for the line passing through the point (2, 0, 4) that is parallel…

A: To find a set of parametric equations for the line passing through the point 2, 0, 4 that is…

Q: Use the maximum magnitude of the remainder term to find the maximum error in the following…

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Q: 3 y = (x² +1) ² Find day dx ²

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Q: Find the directional derivative of the function at P in the direction of v. 1 = √₂ (i+j) f(x, y) =…

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Q: Find the area of the region bounded by the graph of f and the​ x-axis on the given interval.…

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Q: Write an expression for the polynomial of least possible degree graphed below. Leave your answ…

A: The solution is given below

Q: Evaluate the following integral and express in exact form: cos(x/2) sin(x/2) dx

A: SOLUTION-

Q: Solve the given differential equation by undetermined coefficients y" - 8y' + 16y= 12x + 6 y(x) =

A: Given:         y'' - 8y' +16y = 12x+6

Q: f(x)=ax^3+bx find the derivative

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Q: A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of…

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Q: X: 1 2 Y: 2 4 3456 7 9 12 14 What is the correlation coefficient for variables x and y? a..950 b.…

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Q: Find the gradient of the function at the given point. g(x, y) = 12xe/x, (12, 0) Vg(12, 0) =

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Q: ct rit Find the x-value of all points where the function below has any relative extrema. Find the…

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Q: A bank offers a 12% interest to be compounded annually. How much should a teacher deposit now if he…

A: A bank offers a 12% interest to be compounded annually. The teacher wants to receive Php. 15000 at…

Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: 9-x2 x dx

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

Q: Evaluate the following integral: Sºa dx -00x²+1

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Q: derivatives-and-the-shape-of-a-graph and the Shape of a Graph -5-4-3 202. f'(x) For the following…

A: The given graph is of f'.        If    f'&gt; 0 at a point , then  f is increasing.       If  f'…

Q: me Determine the equation of t e 00 te tragen ܘܪܐܐܝ tangent line to y 3- 22+1 at 2:

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Q: Solve the following two Euler's differential equations: (a) x²y" - 7xy' + 16y = 0 (b) x²y" + 3xy' +…

A: The given Euler's differential equations are a) x2y''-7xy'+16y=0b) x2y''+3xy'+4y=0

Q: A barrel is shaped like an ellipsoid with equal pieces cut from the ends by planes perpendicular to…

A: Given a barrel of height 2h and radius at center R and at the has radius r. To find a formula for…

Q: Given f(6)=3, f′(6)=11, g(6)=−1, and g′(6)=7, find the values of the following (a) (fg)′(6)= (b)…

A: Let's solve.

Q: y = (201³ - 6) Find d²y da 3 9

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Q: 4. Solve y 3x 3y + 2y" e using undetermined coefficient. Show all the work.

A: We need to solve D.E.

Q: In 2020, the hourly minimum wage for a City of Madison worker was $11.15. Suppose the hourly minimum…

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