A. Show that f(x, y) = (x-1)(y-2) (x-1)²+(y-2)² 7 (x, y) = (1,2) (x, y) = (1,2) at (1,2). 1 is continuous or non-continuous

Q: √√√(-) True f(x,y) dx dy False - L.T. 1.². f(x, y) dy dr

A:

Q: Using the Runge-Kutta method of order 4, find y for x = 0.1, 0.2, 0.3 given that dy/dx = xy + y²,…

A:

Q: Find the value of c for which the area enclosed by the curves y = c - x² and y = x² c is equal to…

A:

Q: Evaluate fs 2 ds a. 2(sln2 - 1) (In2)² b. 25 (sln2 - 1) (In 2)2 c. 2² (² + 1) 2 d. 25 * (12-1)

A: To evaluate the given integral

Q: If the period T is note equal to 27 but T=2L then f(x) = a + an bn Σ(ancosx + b₂ sin x) n=1 1 2L ao…

A:

Q: Find the Maclaurin Series representation of the function f(x) = x cos(2x). (Hint: If you know the…

A:

Q: x dy-y dx = x3 dx y" Answer: 4x + x4y + x¹y = Cy.

A:

Q: 3-20 Use the Ratio Test to determine whether the series is convergent or divergent. 16. Σ n= (2n)!…

A: This question can be solved using the concept of ratio test for convergence and divergence.

Q: on) solve the Differential en by using vanation of parameters - 24 (+12 yll -24¹ +y₁

A: Please see the below picture for detailed solution.

Q: Find the polar equation for the Cartesian curve ² Or 1 T= cos 2 1 Or=sin @tan 0 2 T = Or= Or T = 1 1…

A: The given cartesian curve x2=y2 we have to find the polar equation

Q: 10. A tank originally contains 380 litres of brine holding 450 N of dissolved salt. Eight litres/min…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: EXAMPLE 5 In an oil refinery, a storage tank contains 2000 gal of gasoline that ini- tially has 100…

A:

Q: π Consider T3 (x), the 3rd degree Taylor polynomial of f(x) = cos(x) centered at a = 4 Use the…

A:

Q: √3+2 px/3 ² √²³ (2² 10 (2 cos 0 - 3 sin 30) de dr

A:

Q: Find f x² sin(x²) dx using the Maclaurin Series.

A:

Q: Solve the following initial value problems: A. y(0) = -3: y= B. y(0) - 6: y= dy dt 2t

A:

Q: Bottom of the page is cut off i cannot see the solution.

A:

Q: Find the curl of the vector field F(x, y, z)= e sin yi - e cos yj.

A:

Q: Match the function with one of the graphs below using horizontal asymptotes as an ald. 4x f(x) = y 2…

A: Let's find horizontal asymptote of given function.

Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

A:

Q: 2. Find from first principle the derivative with respect to x of the function f(x)= Inx.

A:

Q: Two sides and an angle are given below. Determine whether the given information results in one…

A:

Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

A:

Q: ["[" f(2,3) dy dr True False [1 f(x, y) de dy

A:

Q: Evaluate O O In 9 3 2 - In 2 In 2 x² 2 O tan¹ (2) tan¹(1) O ln 2 0 1 3 9 dx. x³ + 1 -

A:

Q: Let g be defined by the equation g(x) = sin 2 dt 1²-1 Show that g'(x): = sec z.

A: Given:       gx=∫sinx0 dtt2-1       Factor -1 from the denominator:       =-∫sinx011-t2dt       The…

Q: at a price of $55

A:

Q: Suppose that the DE y"" (x) + 7y(x) =70 2³ +123 has a solution of the form y = Az³ + B Find the…

A:

Q: The area of a semicircle of radius 1 can be expressed as S√₁-2²dx Use the substitution x = cost to…

A: This question can be solved using the concept of definite integrals.

Q: Write out the first five terms of the sequence. n/n2 +2

A:

Q: with side length a from each corner and folding up the sides. Find a formula for the volume of the…

A:

Q: For which of the following infinite series does the Ratio Test fail? IM8 IM8 k=0 k 5k そそ n=1 (n +…

A:

Q: 4. x³+2x+2 2 x²-1 dx

A:

Q: Consider the function f(x) 12x5 + 45x4 - 80x³ +3. f(x) has inflection points at (reading from left…

A:

Q: H.w2: Use Runge-Kutta Method with (h= 0.1) to solve the eqaution y" + 3xy'-6y=0 with y (0) = 1,…

A:

Q: Question 1 Nondifferentiable graph.png Find the x-values (there are three values) from the graph,…

A:

Q: Consider the function f(x) = 3x² - 6x +5, 0≤x≤ 8. The absolute maximum of f(x) (on the given…

A:

Q: da Find at z = 4 if y = 4z² - 1 and dt da dt 11 > Next Question dy dt = -5. 11

A:

Q: If f(x) = 4x² - 2x + 7, find f'(3). Use this to find the linear approximation to f(x) at x = 3. The…

A:

Q: 4. I Find the general solution of the given system: dx1 dt dx2 dt = 7x1 +4x₂2 =-3x1-x2

A:

Q: For the cost function C(x) = 2950 +670 +0.8x2 and the demand function p(x) = 2010, find the…

A: Given: Cost Function C(x) = 2950 + 670x + 0.8x2 Demand Function p(x) = 2010 Find the production…

Q: The area of a rectangle is increasing at a rate of 4 cm/sec ? while the width of the rectangle…

A: The area of a rectangle is increasing at a rate of 4 cm/sec ? while the width of the rectangle…

Q: dr 3 - 4r - r2

A:

Q: v=√ √31-3j w=i-j gle between v and w; (c) state whether the vectors (a) v-w= (Simplify your answer.…

A:

Q: G A rectangle has its two lower corners on the x-axis and its two upper corners on the parabola y =…

A:

Q: Show the complete solution. Kindly, include the necessary table of values.   2. The population of…

A:

Q: sinx cosx 4 + sin4 x dx

A: The given integral is sinx cosx/(4+sin4x).

Q: limit, if it exists. 5X +8 x--4x - 7 ree of the numerator is equal to equal to the degree of the…

A:

Q: Use linear approximation, i.e. the tangent line, to approximate √49.1 as follows: Let f(x)=√x. Find…

A: Please refer to the image below

Q: Consider the function f(x) = 4-4x² on the interval [-5, 6]. (A) Find the average or mean slope of…

A: The given problem is solved below in detail.