Find the equation of the plane tangent to the following surface at the given points. 2 2 2 x+y-z-81=0: (5,9,5) and (-9,-5,5) The equation of the tangent plane at (5,9,5) is=0.

Q: Find the domain of the function using interval notation. f(x) = -2x (x-2)(x-7) To enter oo, type…

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Q: If z = sin (₁) functions of u and v. дz ди дz Əv and x = = In(u) and y = v4, find the following…

A: Topic = Derivative

Q: The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of…

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Q: 4. Find the exact value of surface area of the solid that is described by the intersection of the…

A: To find the exact surface area.

Q: Given the following graph a. Evaluate f (3). f(3) = Number b. Solve for f(x) = 3. n ril H Submit…

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Q: Calculate the directional derivative of f(x, y) = tan ¹(xy) in the direction of v = -5i + 5j at the…

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Q: Find the sum of the first 14 terms of the geometric sequence 1 9,  1 3, 1,   . (Round your answer…

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Q: Suppose that for a company maunfacturing calculators, the cost and revenue equations are given by C…

A: We have to find the rate of change of cost, revenue and profit.

Q: Estimate the area under the graph of f(x) = x² + 4x + 1 over the interval [ – 3, 0] using five…

A: Here we have given a functionf(x)=x2+4x+1. Now plotting the graph of the given function we get.

Q: 2. Obtain the general solution by the indicated technique: separation of variables 2.1…

A: 2. According to question,2.1 Given Differential equation,2a2-r2dr =r3 sin θ dθ,We have to solve this…

Q: A water tank in the shape of an inverted circular cone has a base radius of 2 m and height of 3 m.…

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Q: 5. Find the equation of a parabola with vertex at the origin whose properties are given below. a.…

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Q: The function f(x) = 2x³ - 45x² + 300x + 9 has one local minimum and one local maximum. Use a graph…

A: Topic - Local extrema's of a function We are given an equation, f(x)=2x3-45x2+300x+9And it's known…

Q: Evaluate f(x) = 3 sin x + 5 cos at x = π/3. 1. f(π/3) = 4 4√3 2. f(π/3) 3. f(π/3) 3√3 4. f(π/3) =…

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Q: Find the absolute maximum and absolute minimum of the function x3 3 f(x) = 1 7x² 2 + 10x - 2 over…

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Q: Grain pouring from a chute at the rate of 12 ft3/min forms a conical pile whose height is always…

A: How fast is the height of the pile increasing at the instant when the pile is 8ft high? change in…

Q: Find the value of the constant C' for which the integral converges. Evaluate the integral for this…

A: We have to evaluate the integral.

Q: Convert the following standard form to general form of parabola. a. (y+1)²=-2(x+2)

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

Q: (c) You are given the point (3, 2) in polar coordinates. (i) Find another pair of polar coordinates…

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Q: V₁² W V4 0 -21 V2 V3, and v4 are given below. -9 Then H and K are subspaces of R³ In fact, H and K…

A: we will find the required.

Q: Consider the vector field Vf where f(x, y) = Evaluate 557² 2 + 2xy + 3y². Vf. dr along the curve C:…

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Q: Given the function z = In(x - 2y), find the equation of the tangent plane when (x, y) = (3, 1) in…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) J- sin(2x) 14 + cos²(x)…

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Q: Find the derivative (be sure to simplify): f(x) = sinh(ln(x²))

A: Given query is to find the derivative of the expression.

Q: Find the slope of the curve x3 = (y - x2)2 at (1,2).

A: Topic:- application of derivatives

Q: Find the gradient of the function y at x = 4.

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Q: Given function f(x) = ¹, X x = 0 (a) Find the slope of the curve y = = at X (b) Where does the slope…

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Q: 7. Set up but do not evaluate a triple integral using spherical coordinates to find the volume of…

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Q: 2. Convert the following standard a. (y + 1)² = -2(x + 2)

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

Q: 3. The area of a circle increases at a rate of 47 cm²/s. How fast is the radius changing when the…

A: We can find the required answer in the below steps using the given data.

Q: S sin4xcos4xdx

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Q: -Suppose you have a box centi C(a, b, a+b), having a length (along x-axis) of Za units, width (along…

A: a = 5, b=2 O is the origin, OX is the x-axis, OX = 2a units = 2*5 = 10 OY is the y-axis, OY = 4b…

Q: Use linear approximation, i.e. the tangent line, to approximate √64.4 as follows: Let f(x)=√x. Find…

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Q: Find the equation of the tangent plane to at the point (0, 5, 34). z = z = e² + y + y² +3

A: The given equation is; z=ex+y+y2+3 Point (0,5,34).

Q: Find the intervals on which the graph of f is concave​ upward, the intervals on which the graph of f…

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Q: 6) Find the area of the part of the sphere X² + y² + Z² = 4 that lies within the cylinder X² + y² =…

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Q: What is the rate of change of x with respect to y when the bottom of the ladder is 4 m away from the…

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Q: Use the properties of logarithms to expand the logarithm as much as possible. Rewrite the expression…

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Q: What is the slope of the line tangent to the curve x² + y2 = 1 and parallel to the line y = - 2 ?…

A: Given query is to find the slope of the tangent line.

Q: year-end bonus of $25,000 will generate how much money at the beginning of each month for the next…

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Q: Let F(x, y, z) = x³i+y³j+z³k. Compute the following: (i) V.F (ii) V X F

A: i) Given:       Fx,y,z=x3i+y3j+z3k then         ∇·F=∂∂xx3+∂∂yy3+∂∂zz3                 =3x2+3y2+3z2…

Q: Find the area under y = x(e)^(-x)^(2) for x > 1

A: The given curve y=xe-x2 We have to find the area under the curve for x>1.

Q: Question 1 Evaluate the integral. 2xsinxcosxdx Ax cos 2x - sin 2x + C B-x cos 2x + sin 2x + C C) -x…

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Q: Evaluate each expression, using the values given in the following table, X (a) (gof)(-2)- (b)…

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Q: If the rate of change of a population is directly proportional to the square of the population and…

A: If the rate of change of a population is directly proportional to the square of the population and…

Q: Find the value or values of c that satisfy the equation C= f(x) = 4x + 4 X [16.16 f(b)-f(a) b-a (Use…

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Q: 7. Determine the standard equation of the parabola in the figure given only its focus and vertex.…

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Q: Find the average value of the function y = 35 - 2x on the interval [0, 4]. O 31 10 O 20 O None of…

A: The Answers are given below

Q: X Dx f¹2dt 4+t -X

A: We have to differentiate the given equation.

Q: Problem 5. they all start at n = 1. List the first six terms of the sequence given by the formula.…

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