Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if (x, y) + (1,1) f(x, y) = {vx-vỹ () if (x, y) = (1,1)

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A:

Q: 1 Use SUBSTITUTION to evaluate the definite integral to three decimal places. xp- 2x +4

A:

Q: Question A vertical cylinder is leaking water at a rate of 8 m³/sec. If the cylinder has a height of…

A:

Q: Find the area of one petal of the rose curve r = 3 cos 30.

A: Let's find.

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(-5, 7,…

A:

Q: Compute the first four partial sums S1, .., S4 for the series having n th term an starting with n =1…

A: In this question we have to find partial sum.

Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction I|v|| =…

A:

Q: 4 -2x?y = 1 r = sin(0) (b) Pick a coordinate that lies on the graph of the equation you picked from…

A:

Q: Solve the equation: (2r – xy? – 2y + 3)dx – (x²y + 2x)dy = 0 x4 – 2ry? – 4xy + 6x = c O x* - x²y² –…

A:

Q: The other type of question in chapter 7 is solving trigonometric equation. We will not be practicing…

A:

Q: 17. SHOW ALL WORK Use De Moivre's Theorem to evaluate the expression. Write the result in standard…

A: Given,              1-i4To find : Use De Moivre's theorem to evaluate the expression.We know that,…

Q: Set up and evaluate the integral for finding the area and moments about the x- and y-axes for the…

A:

Q: Find the arc length of the parametric curve. x = e', y = et, z = v2t; 0<t < 8 L ||r'(t) × r"(t)||…

A: Given parametric curve x=et  , y=e-t  , z=2 t   ;  0≤t≤8

Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence…

A: an=nqen limn→∞an=limn→∞nqen = 0 [when x tends to infinite ax&gt;xa (where a is positive constant)]…

Q: Determine

A: We have to determine the given series is converges or diverges

Q: An appropriations bill passes the U.S. House of Representatives with 59 more members voting in favor…

A:

Q: 1) Find the area of the region that lies inside the curve r =1-sin 0 and outside the curve r = 1.…

A:

Q: The other type of question in chapter 7 is solving trigonometric equation. We will not be practicing…

A:

Q: y(x)=asin2x+bcos2x, where a and b are arbitrary constants, is solution of the differential equation…

A:

Q: 3) Given f(x) =-2x -2x-2, find the absolute maximum value over the interval [0,6].

A: We have to slove the above question and find absolutely maximum value

Q: What is the area of the region bounded above by y = -x- + 8 and below by y = x? 54 $2 14 1 23 4 5 64…

A: This is a problem related to integration. Based on the formula of area bounded by given region we…

Q: 15.lf f(x)=Vx f(x)-f(16) The lim x→16 x-16

A:

Q: 3. y" +4y = 0; yıi =cos 2x, y2 = sin 2x; y(0) = 3, y'(0) =8 4. y" + 25y = 0; yı = cos 5x, y2 = sin…

A: Note : "Since you have posted multiple questions, we will solve first question for you. To get…

Q: The radius of the circle 2x? + 2y? – 4 = 0 is equal to 2 units. O TRUE O FALSE

A:

Q: 1) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 1.1., # 37 or from your…

A:

Q: Find u · v, u· u, ||v||2, (u· v)v, and u · (3v). u = (4, -2, 5), v = = (0, 6, 3) (a) u V (b) (c)…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: 5- 3x? Evaluate lim x-00 (2-x) (x+ 2) does not exist O NONE OF THESE -3 3 O O o O O

A:

Q: Convert the point (r, 0) from Polar to Rectangular Coordinates (x, y). 1. (3, 7/6)

A:

Q: Lets compute a derivative in reverse! Given the function f(r) = e² + sinhr + + z find a function…

A:

Q: Question For the function f(x), whose graph is shown below in blue, find lim f(x). The red vertical…

A:

Q: sequential convergence Lim 3-8n h-oo n+2

A:

Q: What is the differential equation of the given 1 parameter family of solutions?

A:

Q: - 2 Evaluatelim x- 8x2-7x-8 O 1/9 O 27 O NONE OF THESE 1/12

A: To evaluate: limx→8x3-2x2-7x-8

Q: Solve the area of the surface of revolution generated by revolving the arc of the curve, x=y° from…

A:

Q: Use the ratio test to discuss the Con vergence or divergence of the seríes which s the Sum from n1to…

A:

Q: (0,0,0) (1,1,1) C2 C.

A:

Q: Find the radius of convergence, R, of the series. (x + 6)" 6" n = 1 R = Find the interval, I, of…

A: Consider the power series           ∑n=1 ∞ an(x-a)n then , series convergent if x-a&lt;R , where , R…

Q: Find the area of the region between the graphs of f (x) = 3x3 – x² – 10x and g(x) = -x2 + 2.x, %3D -…

A:

Q: 7) Determine the particular solution to the differential equation y 3x-2 that passes through the…

A:

Q: The hypotenuse of a right triangle is 45 in. The sum of the lengths of the legs is 9 in. Find the…

A: The hypotenuse of a right triangle is 45 in.The sum of the lengths of the legs is 9 in.

Q: dx xV2ax – x2 ах

A: This is a problem of integration. Based on the general formula we will solve the question.

Q: Consider the following function. f(t) = 4t + 5 Find its average rate of change over the interval [1,…

A:

Q: 3- x 3) dx → S2xe* dx

A: To evaluate the given integrals.

Q: H = 33(10VV - v + 10.45) where v is the wind speed (in meters per second). (a) Find dH dv dv dH in…

A:

Q: Question For the function given below, which statements concerning Rolle's theorem are true? f(x) =…

A:

Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction ||v|| =…

A: A vector v with given magnitude in the direction of u is given by v.uu.

Q: Use limits to determine all the linear asymptotes of 3x2 – 5 if a1. a² + 2x – 3'

A: Let's find.

Q: 4. So -dy Vy+1

A: To evaluate: ∫01yy3+1dy Substitute y3=u2⇒13y-23dy=2u du⇒13u4dy=2udu⇒dy=6u5du. As y→0⇒u→0, y→1⇒u→1…

Q: Find the length of the arc from 0 = 0 to 0 = 2n for the cardioid r = f (0) = 2 – 2 cos 0.

A: Solution if r=fθ  has a continuous first derivativefor α≤θ≤β then length of polar…

Q: The world population at the beginning of 1990 was 5.3 bilion. Assume that the population continues…

A: