Show that the function g(x, y) = is not continuous at (0,0). xy 2x² + y²¹ 0, (x, y) = (0,0) (x, y) = (0,0)

Q: Find the area of the region R under the curve of f(x) = from x= -1 to x = 1.

A: f(x)=e(1/2)x from x=−1 to x=1

Q: Find a parametric representation for the part of the cylinder y2 + z2 = 64 that lies between the…

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Q: Consider the function F(x) = [*__cos(1²) dt. (a) Compute F(-√√T).

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Q: The grid on the right shows the graphs of several functions f(x) whose slope at 8x each x is Find…

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Q: (d). find the y-intercept. (e). Graph f(x)=-4x²-24x-32. Include a table of values. (f). Give the…

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Q: Find the area of the region between the curve and the x-axis. f(x)=e*-6 from 0 to In 6

A: Tofind the area of the region between the curve and the x-axis.

Q: Use a Riemann sum to approximate the area under the graph of f(x)=x on the interval 3≤x≤5 using n =…

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Q: At what value(s) of x on the curve y=-7+90x^3-3x^5 does the tangent line have the largest slope?

A: y=-7+90x3

Q: Determine the following indefinite integral. 5-6 sin¹ (2) cos(x) dx

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Q: (i) Find the area of the shaded region. 0 (1, 1) y=√√√2-x 2 x=y4

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Q: Determine the integral by making the appropriate substitution. 1 x In 7x²

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Q: Determine the polynomial function, f(x), with the smallest possible integer co- efficients that has…

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Q: Write an equation of the graph in the final position. The graph of y= 2* is shifted 4 units left and…

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Q: Express the vector P₁ P₂ in the form v=v₁l+V₂j+V3k if P, is the point (0,5,0) and P₂ is the point…

A: given  and

Q: F(x) F(2) (5) F(7) - L² (t³ + 6 t F(x)= (t³ + 6t-5) dt

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Q: Build the tangent line approximation (linear approximation) to 6 -5 0 2 3 4 5 6 7 8 9 10 11 12 f(x)…

A: To build the tangent line approximation (linear approximation) to .

Q: H Use Stokes' Theorem to evaluate Sc F. dr where F = (x + 6z)i + (5x + y)j + (8y-z) k and C is the…

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Q: (4) Find the maximum and minimum values of f(x, y) = xy on the ellipse x² - xy + y² = 1.

A: The given equation of function  Let

Q: Find all the antiderivatives of the following function. Check your work by taking the derivative.…

A: Given,

Q: I had that first answer but it was wrong and I also had 2 sin theta cos theta but as my second…

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

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Q: A) Consider the vector field F(x, y, z) = (yz, -9xz, -8xy). Find the divergence and curl of F.…

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Q: At time t, the position of a body moving along the s-axis is s=13-1512+72t m. Find the body's…

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Q: C Determine Ax and the midpoints of the subintervals formed by partitioning the given interval into…

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Q: Electric charge is distributed over the disk x² + y² ≤ 3 so that the charge density at (x,y) is o(x,…

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Q: (f) (g) Find the absolute maximum and absolute minimum of g(x). On what interval(s) is g(x) concave…

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Q: Find a parametrization of the line in which the planes x+2y+4z=-4 and 2x+3y+6z= -7 intersect. Find…

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Q: Problems 1-10, multiple choice. 1. What is the average value of y = e* on the interval [2, 7] ? A.…

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Q: Use logarithmic differentiation to find the derivative of y with respect to the independent…

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Q: Find the area of the parallelogram whose vertices are given below. A(-1,2) B(4,0) C(12,1) D(7,3) The…

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Q: The velocity function, in feet per second, is given for a particle moving along a straight line. 3…

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Q: Find the exact value of the integral using formulas from geometry. (3 (3+x)dx a) Write which…

A: We have to find the exact value of integral using formula from geometry.Given integral Here…

Q: At time t=0, a particle is located at the point (1,5,4). It travels in a straight line to the point…

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Q: Find F as a function of x and evaluate it at x = 5, x = 7, and x = 9. F(x) = F(5)= F(7) = F(9) =…

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Q: 3. g(x) x² +5

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Q: (d) If g(x) is an odd function, then g(x) dx =

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Q: d) Write an expression that represents the approximate value of g(x) for a generic value x in the…

A: The graph of the function g'(x) is shown as,

Q: Evaluate the following definite integral: [²22 (2² 1 2x (x² + 1)² dx Enter your answer as an exact…

A: Let

Q: Find all solutions of the equation in the interval [0,2+). 2 sin 20-3 sin 0+1=0

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Q: Write the following expression in expanded form. +5 log X+7

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Q: x+6 (x + 2)2 dx

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Q: As a preparation for the long bright summer days, Dr. Acula plans to store gourmet plasma in closed…

A: We have to use the concept of derivatives

Q: 17. The amount, A, of 108 grams of a certain radioactive material remaining after years can be found…

A: Given that the amount A of 108 grams of a certain radioactive material remaining after t years is

Q: Determine the integral by making the appropriate substitution. 1 2 x In 3x dx ⠀⠀

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Q: Use symmetry and the fundamental theorem of calculus to evaluate the following integrals. Question 8…

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Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

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Q: Let S be the solid that lies between the paraboloid z = x² + y² and the sphere x² + y² +z² = 2. (a)…

A: Given that  S is the solid that lies between the paraboloid and the sphere The graph of solid

Q: Hi b and c are incorect

A: From the given table

Q: (i) Find the derivative of the function. esin x COS X In(1+2v) dv.

A: To find the derivative of the following function.

Q: Use the table of values of f(0) = 0 f(0) -0.1 -7.6484 -0.01 99.7551 cos (70) 0 to estimate lim f(x),…

A: Limit does not exist when the left hand limit and right hand limit is not same.