Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z? (4, 5, 3) Vf(4, 5, 3) = Find the maximum value of the directional derivative at the given point.

Q: Find the equation of the tangent line and the normal line of the curves at given point 1. x? + y? -…

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Q: V3x+10 - 4 Evaluate lim x+ 2- x2- 4x + 4

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Q: f(x) = / sinx cos x

A: The objective is to flnd the derivative and slmpify.

Q: (e2y – y) cos a = e" sin 2r, y(0) = 0

A: Solution is given below:

Q: A company has identified that the revenue R for a particular product is given by the function f(x) =…

A: topic - application of derivatives

Q: |(1 - 4x4 + x)/x dx = 1/(2x2) + 2x² - x + C Select one: O True O False J(4csc?x -3sec2x) dx = -4cotx…

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Q: Given: -8 17 cose 15/17 -8/17

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Q: Find the sum of the critical numbers of f(x) = 3x4 - 4x3 +2. %3D Answer:

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

Q: Each side of a square is increasing at the rate of 8 cm/sec. At what rate is the area of the square…

A: We have to find the increase of area

Q: From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an…

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Q: 3dt 1. (8) +1 2t+

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Q: Find the dimensions of a rectangle with a perimeter of 140 feet that has the maximum area. The side…

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Q: |(sinx/cos2x)dx = sec x + C %3D Select one; O True O False 16x e2^3+1 dx = 3e3+1 + C Select one…

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

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

Q: Find, correct to three decimal places, the point on the curve y = 9 In x + e at which the tangent…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

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Q: Find the Gauss quadrature rule for f(x)dx z wof(xo) + wif(x1) + wzf(x2). Nodes: Xo = X1 = X2 =…

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Q: 1„2 The graph shown is f (x) = ±x². 4 3 21 1 54 3-2 -14 1 2 3 4 5 -2 3 4 If g(x) = `f(t) dt, what is…

A: This is a problem of antiderivative function. Based on the general formula we will answer the…

Q: V25x² -69 – dx

A: We will find the integral as following.

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

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Q: 4. V40-4v-v² dv – 4v

A: This question can be solved by using the concept of some special integrals.

Q: Find the magnitude of the vector V= (-1,3). 10 10 8 22

A: Given V¯=-1,3 To find magnitude of vector

Q: - ſ csc²e cot êī – 5 cot ê dê

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Q: 2. The function g(x) is defined for -3Sx5 3. The behaviour of g'(x) and g"(x) is given below.…

A: A)-3<x<-2, g'(x)<0and-2<x<1, g'(x)>0Function decreases over (-3, -2) andincreases…

Q: a- Described the order of integration when you have a double integration.

A: Simplify the theory.

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

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Q: 30

A: Here, just to find the angle between F1 & F2.

Q: 4. f(x) = sin xand g(x) = 2x 5. f(x) = x² + cosx and g(x) = 3x + 4 Guide Questions: 1. How did you…

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Q: Find the equation of the tangent line and the normal line of the following curves at the given point…

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Q: estion Evaluate:S sin (3x) cos³(3x) dx r answer estion Ising Trigonometric Substitution, evaluate: -…

A: Solution:

Q: Consider the following. x = t, y- In(t) (a) Eliminate the parameter to find a Cartesian equation…

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Q: Given: -8 17 sece = -17/15 17/8 -17/8 17/15

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Q: Suppose the position of a particie is given by parametrc equations x(e) = -3 and y(t) = 2?. (a) Find…

A: The given data is: xt=t3-3yt=2t2  (a) To find the particle's position (x,y) at t=3

Q: 3. Which of the following is the solution to sin a +1 = 0? O x = 0 + 360k O x = 180 + 360k O x = 90…

A: Simplify the equation.

Q: Match the differential equation with its direction field. y' = sin(10x) sin(10y) y \ 20y 0.34 15 0,1…

A: Here, to match the graph of the given differential equation: y'=sin(10x)sin(10y)

Q: From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an…

A: Explanation of the answer is as follows

Q: Find the domain and range

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: We need to find minimum distance.

Q: Suppose that fis continuous and that / f(x)dr=4 and / s(x) dr=7, Find / 45 (x) dx A 20 B 28 16 12

A: using property∫acf(x) dx=∫abf(x) dx + ∫bcf(x) dx∫-33f(x)dx +∫36f(x)dx=∫-36f(x) dx4 + ∫36f(x)dx…

Q: 23. Exterior angles on the same side of the transversal form a lincar pair. 24. Vertical angles are…

A: 23. True True  here G+D=180  and A+F=180  24. False   vertical angles are just equal to each other ,…

Q: How do I find the area of the region in the first quandrant bounded by the line y=4x, the line x=4,…

A: Here we have to find the area of the region in the first quadrant bounded by the line y=4x, the line…

Q: Using Integration by parts, evaluate: ſ xVx + 1dx Your answer

A: As per our guidelines we are supposed to answer one question, kindly repost the remaining question…

Q: Streaming Music Consumers are spending more on music from digital sources than they do on CDs.…

A: f(t) =3.7+ln(t+1)(a)in 2012 , t=0f(0)= 3.7 +0.84 ln(0+1) = 3.7+ln1=3.7+0f(0)=3.7Amount spent by…

Q: Find a positive number such that the sum of the number and its reciprocal is as small as possible

A: Second Derivative Test :   Firstly find critical point of f(x).i.e, f'(x)=0 and find the value of…

Q: What is the value of csc(0) if the terminal side of the angle 0 intersects a circle at the point…

A: At first we want to find radius of the circle.

Q: Given vectors a = (-1,-2),5= (-2,3), c= (3,-1),đ = (-3,2) find the dot product of 5 and d. -12 -1 12…

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Q: Suppose the position of a particle is given by parametric equations x(t) = t3-2 and y(t) = 4t2. (a)…

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Q: Given: -8 17 csce = O 17/15 -17/15 17/8 -17/8

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Q: After substitution is performed, what is equivalent to /, x sin x² dx , 3 sin u du 8 sin u Li du 3 L…

A: solution is given below

Q: 9. The region bounded by the given curves is rotated about the specified axis. Sketch the region and…

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