Find the linear approximation of f(x,y) = 8 - x² − 3y² at (2,2). Then use the approximation to approximatef (0.85, 1.01).

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A: We have to find the value of h'(1).

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Q: Are there any points on the hyperboloid 22² + y² − 2² = (3) gent plane is parallel to the plane 22-…

A: Given    plane  2z=2x-3y2x-3y-2z=0   the direction ratios of the normal to the given plane : ( 2 ,…

Q: Graph the system of inequalities. Then find the coordinates of the vertices. y-3x - 3 y + 3x ≥ 9 y ≤…

A: We have to find co-ordinates.

Q: Two sides of a triangle are 14 and 4. Find the size of the angle θ ​(in radians) formed by the sides…

A: we will find the required.

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

A: The given region is bounded by the curve y=16-x2 and the x-axis. We have to find the volume of the…

Q: The profit function of a business is given as P (x) = −x2 + 54x + 70. How many units must be sold to…

A: Please see the below picture for detailed solution.

Q: Find the absolute maximum and absolute minimum values of f on the given interval. X x²4 [0, 5] +…

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Q: r(t) = ti + t²j+k₁ t₁ = 2 to: to 5

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Q: Evaluate the integral. (Use C for the constant of integration. Remember to use absolute values where…

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Q: 3) f(x) = 2 . -6 -4 -2 H x Ay 20 18 16 144 12 10 8 6 4 라 2 4 6 X

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Q: S3 f(x) dx = −3 and 2₂9(x) dx = -2, what is the value of f(x)g(y) dA, where D is the rectangle: 3 ≤…

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Q: Write an equation for a rational function with: Vertical asymptotes at x = -2 and x = -5 x…

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Q: Sta tan³ xsec³ x dx

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Q: (0) Σας (3) COS n=1

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Q: (b) Find the co-ordinates of the turning points of the following function: y = 3x4 16x³ + 24x² - 12…

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Q: Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = x - In (8x)…

A: interval [12,2]

Q: an object is removed from a furnace and placed in an environment with a con F. Find the core…

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Q: → → Find the dot product between vectors a and b, given →→ →→ → d=3i-jandb=2i+j+4k

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Q: Find the directional derivative of f at the point P in the direction of a. a=i-j f(x, y) = 6x³ —…

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Q: Use either the shell method or the disk/washer method to find the volume of the solid of revolution…

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Q: Isn't the derivative lnx^2 = 2x/x^2?

A: We have to find the derivative of lnx^2.

Q: Year 1950 1960 1970 1980 1990 Rate of change (million people per year) 27 42 59 79 96…

A: Given that , Year 1950 1960 1970 1980 1990 Rate of change (million people per year) 27 42 59 79…

Q: ind the relative extreme points of the function, if they exist. Then sketch a graph of the function.…

A: In this question, we want to find the relative maximum and minimum point of the given function f(x).

Q: Graph the system of inequalities. x≤2 y≥3-3x Use the graphing tool to graph the system of…

A: x≤2 line x=2     y≥3-3x draw line y=3-3x x y 0 3 1 0 check for orgin y≥3-3x0≥3-3(0)0≥3…

Q: Find (5x + 2y)dA where R is the parallelogram with vertices (0,0), (5,3), (-4,2), and (1,5). R Use…

A: The vertices of parallelogram is given as , 0,0,5,3,-4,2,1,5 and x=5u-4v , y=3u+2v find ∫∫R5x+2ydA=?

Q: 2 6² 6² S (3x + 4y) 5dxdy 0 Find

A: We need to evaluate :

Q: Solve for x: 103-6-32x-2 X

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Q: J exp (x+3) dr

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Q: A conical tank has height 3 m and radius 2 m at the base. Water flows in at a rate of 2 m^3/min.…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: To find the maximum rate of change of f at the given point  and the direction in which it occurs.…

Q: The cost c in terms of the quantities 9₁ and 92 produced of good 1 and good 2 is given by c = 200 +…

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Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A: We have given the dimensions of the cardboard sheet i.e.   length= 11 in.  breadth = 7 in .

Q: Transformation by trigonometric identities & integration by parts. Evaluate each of the following…

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Q: What is lim 5 + X 2 x→+∞ ex-1 -?

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Q: Fill in the missing values such that the final term is pulled out of the summation. Ex: 5 15 Σ; = Σ…

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Q: 2

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Q: Gonzalez Manufacturing borrowed $30000. Part of the money was borrowed at 10%, part at 12%, and part…

A: Let the money borrowed at 10 % = x Let the money borrowed at 12 % = y Let the money borrowed at 14 %…

Q: 14₁ 6₁1) (1x) = +9=2 #1. Find T₂(x)) Taylok polynomial

A: Please see the below picture for detailed solution.

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe-x2/162,…

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Q: Find two numbers, and y, whose difference is 42 and whose product is a minimum. (Answer as a common…

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Q: The general form of an antiderivative of the function f(x)=csc(x)(5csc(x)−6cot(x)). is F(x)=

A: f(x)=cscx(5cscx-6cotx)we know∫csc2xdx=-cot(x)+c

Q: A swimming pool is circular with a 40-ft diameter. The depth is constant along east-west lines and…

A: Given: A given swimming pool is circular with a 40 diameter and radius 20. since height varies from…

Q: n=1 ncosan ૦૬, Itn³ 3

A: Solution: ∑n=1∞πcos2(n)1+n3Apply the constant multiplication rule:=π·∑n=1∞cos2(n)1+n3

Q: A lamina occupies the part of the disk x² + y² ≤ 36 in the first quadrant. Find its center of mass…

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Q: f(x)= In(2+ sin(x)), 0≤x≤ 2x Find the interval(s) on which fis concave up. (Enter your answer using…

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Q: 3. Determine the intersection (if any) of the following planes. Show your work clearly ₁: 2x + 3y z…

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