Suppose that f(x, y) = x' + y – 2xy Then the minimum is

Q: 1. A line passes through the points A(2, 3) and B(-2, 1). Find a vector equation of the line. [x, y]…

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Q: The boundaries of the shaded region are the y-axis, the line y = 1, and the curve y = VT. Find the…

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Q: Find the area of the region between the curves 4x + y? = 12 and z = y. Area between curves =

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Q: To find the distance across a small lake, a surveyor has taken the measurements shown. Find the…

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Q: Evaluate the given limit |. lim %3 1- x2 2. lim CosX

A: 1. limx→0+1x-1ex-12. limx→∞x1cosx

Q: Find the vo lume oF the solid OF revolution when the regiON bounded by y = x +1, the solid X-axis,…

A: Given problem:- Find the volume of the solid of revolution when the region bounded by y = x + 1 the…

Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y = x°, y =…

A: Here we have to find the volume.

Q: The limit lim (x In( cos x-00 is an indeterminate form of type 0 0o. Select one: True False

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Q: Let f(z) then for all real number the power representation of f is Select one: O True O False

A: Recall : 11−x=∑n=0∞xn=1+x+x2+x3+…

Q: (1 - cosx) dx Evaluate: cosx(1 + cosx)

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Q: Use properties of limits to find the indicated limit. It may be necessary to rewrite the expression…

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Q: Write the composed trigonometric function sin (arctan x)sin (arctan x) in terms of x. Explain your…

A: In this question we have to find the function in terms of x.

Q: dx (9 – 4.x²)³/2 2,3/2

A: Use substitutions to make it more simple

Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of…

A: The given integral is ∫x(9-7x2)5 dx

Q: Suppose that a cylindrical can is designed to have a radius of 1 in. and a height of 5 in b the…

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Q: 9. (2xy – sec?x)dx + (x² + 2y)dy = 0 10. (x + 3x³ sin y)dx + (x* cos y)dy = 0

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Q: 3) Explain why the Cartesian equation 2x– 5y+ 3z = 2 does not describe the plane with normal vector…

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Q: x+729 If k(x) = complete the table and use the results to find lim k(x). X+9 X-9 -9.1 -9.01 -9.001 -…

A: Using L hospital rule find limit

Q: Classify the statement as either true or false. lim 2 4 X4 Choose the correct answer below. true…

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Q: Find the derivative of f(x) = (2x^2-x-1)(sqrt of x) %3D

A: A detailed solution is given below.

Q: Σ Preview i=1

A: We will use sigma notation.

Q: PART C 15. Use the definition of the derivative to evaluate each limit. e2+h – e? 1 a. lim h h→0 b.…

A: Given problem:-

Q: Problem 4 Use the rules of differentiation to to find the derivatives of the function (a) f(x) =7–…

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Q: Find the equation for the horizontal asymptote of the graph of the function. (If an answer does not…

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Q: Find the limit. lim ---X +4 Step 1 1 x+ 4 as x approaches -4 from the left. Note that we cannot…

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Q: Find, by slicing, the volume of a cone whose height is 5 cm and whose base radius is 1 cm. Slice the…

A: The slicing cone has height 5 cm and radius 1 cm

Q: What number is in the tenths place - 7.2431?

A: Given Number                           7.2431

Q: To find two real numbers whose sum is 23 and whose product is maximum, we should find the maximum…

A: sum of number is 23 let a number = x  other number is 23 - x

Q: Jse symmetry arguments or similar to find the total charge in sphere of radius Rothat has charge…

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Q: Suppose that f(z, y) – e ¯4r² - 4y² - z + 2y Then the maximum is

A: The given function is: f(x,y)=e-4x2-4y2-x+2y Here,…

Q: The solid shown in figure consists of cone of radius (r) and height (h) and a hemisphere of radius…

A: Given : h(t) = 2t2-6 (cm)              r(t) = 8-t2 (cm)                t= 2 sec

Q: Suppose that f(x, y) = x? – zy + y² – 3z + 3y, with domain D constrained by the lines y = z, y = 0 ,…

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Q: Find the arc length parameter along the curve from the point where t= 0 by evaluating the integral s…

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Q: Construct a table and find the indicated limit. Vx +2 If h(x)= x-8 then find lim h(x). x-8 Complete…

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Q: 5+ 4. 2 1+ -5 -4 /-3 -2\1 1 5 -1 -2 -3 -4 -5 + 3.

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Q: The volume of the solid obtained by rotating the region enclosed by y = 12, T = 2, I = 6, y = 0 |3|…

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: Given:   f(x) = 7x+1    ,  a = 5

Q: 12. Find the maximum and minimum values of each function. Graph each function. а. у %3D е* + 2 b. у…

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Q: r(10,3,3) dx (1,1,1) dy dz. - -

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Q: x’y? If z , show that x=+ y- 3z x+ y ôx ây a²z ô²z = 0 if z= Tan 2.xy x² – y? Show that âx² ' ây²

A: A detailed solution is given below.

Q: V1. y=x' +1, the axes, x=3; 0X 1 y =-, , y-axis , y=1 & y =3 ; OY

A: Here we have to find the volume.

Q: Find the arc length parameter along the curve from the point where t= 0 by evaluating the integral…

A: Given problem:-

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A: Use derivative and unit tangent formula for finding it.

Q: Find the slope of the tangent line to the curve - 2x2 + 3xy + 4y° 3 242 at the point (- 1, 4).

A: Solve the following

Q: fi(x)-2• sin(x) -3- R 3- 5- 3.* 4. 4 2 -2

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Q: Write a in the form a = a-T+ anN at the given value of t without finding T and N. %3D r(t) = (4 e*…

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Q: b). Using gamma function, evaluate Sx6 e-2x dx

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Q: dy given the dx Use implicit differentiation to determine equation x? + y² = 4. dy dx

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Q: Find the slope of the tangent line to the curve (a lemniscate) 2 (z? + y?)° = 25(x² – y²) at the…

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Q: 1. An airplane is flying towards a radar station at a constant height of 6 km above the ground. If…

A: Let us assume that radar station to be at ground level. Then representation of plane and radar can…