The following chart shows student population in a certain elementary school over a 5 year period. 2010 2011 2012 2013 2014 Year Students 640 695 735 765 785 What is the average rate of change in the number of students from 2010 to 2012? Students/Year What is the average rate of change in the number of students from 2011 to 2014? Students/Year

Q: Find the gradient of the function at the given point. Function g(x, y) = ye-x Vg(0, 9) = Point (0,9)…

A: Given function: g(x,y)=ye-x

Q: Determine whether the given set of functions is linearly independent on the interval (-∞0,00). f₁(x)…

A:

Q: (2xy - x + 2y - 1) dx + (4x²y² - x² + 4xy² - x) dy = 0

A:

Q: (4x²y² - x² + 4xy² - x) dx + (2xy + x + 2y + 1)dy = 0

A:

Q: Find the second order derivation for y = e-3x².

A: d2dx2e-3x2

Q: Sketch the region of integration. [ [² x√ 1 + y³ dy dx

A: The answer as follows:

Q: Find y" of y=- y" = y" = O y" = y" = X-1 2 (x-1)² 2 (x - 1)³ 1 (x - 1)³ -2 (x - 1)³

A: Topic = Derivative

Q: Given the unit circle, x^2 +y^2=1. Sketch the unit circle and pick a point K(a,b) on the unit circle…

A:

Q: =S • I = dx (x²+9²)² 2 ans ? tr 493

A: This is a problem related to integral solving using residual theorem. Please follow the procedure…

Q: eley y³ dx + (27x-x³) dy, where C₁ is the unit circle given by r(t) = cos(t)i + sin(t)j, 0 ≤t≤ 2m.…

A:

Q: Find the general solution of the given higher-order differential equation. y"" + 4y" - 9y' - 36y = 0

A: Follow the procedure given below.

Q: and the partial fraction decomposition. -2x-9 2 x -3x -2x - 9 2 X - 3x - SERT 0

A:

Q: Use a double integral to find the volume of the indicated solid. 16 15 8 TOHNWASSL 00SOTNWAS 14 13…

A:

Q: Expand the function (Express numbers in exact form. Use symbolic notation and fractions where…

A:

Q: improper iterat 1/x3 y dy dx

A:

Q: Example 13 Les A-[³3] and [3] A= B= Find AB and BA if they exist.

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

Q: Find the average value of the function over the given solid. The average value of a continuous…

A: Average value of the function = 1V ∫∫∫E f(x,y,z) dzdydx .

Q: Use the equation Σ x" for [x] < n=0 (Express numbers in exact form. Use symbol 6 1 - x4 Σ 1 1-x Σ…

A:

Q: Find the interval of convergence of the series. (5x) n².4" n=1

A:

Q: Step To sketch the graph of f(x) = 4x - x², first construct a table of values by evaluating the…

A:

Q: 5 Find the equations to both lines through the point (2,-2) that are tangent to the parabola y = x²…

A:

Q: Estimate the slope of the graph at the points (x₁, y₁) and (x2, Y₂). At (x₁, y₁), slope At (x, y₂),…

A: We know:- sllope of a line passing through two points =y2-y1x2-x1

Q: The length and width of a rectangle are measured as 38 cm and 34 cm, respectively, with an error in…

A:

Q: Part 2 of 8 The equation x³y-x-9y=0 is in the form of ax² + bx+c = 0. The solution set for x is…

A: Let's solve given equation.

Q: Examine the function for relative extrema and saddle points. (If an answer does not exist, enter…

A:

Q: 6. Evaluate the following real integrals by residue theorem 3 • I- 88 151 +47 O dx (x²+1)(x² +9) ans…

A:

Q: (a) Area = ſ dx dy (b) Area = = [[ JJ dy dy dx

A: Follow the procedure given below.

Q: Find div(F x G) = V. (F x G). F(x, y, z)= i + 7xj + 8yk G(x, y, z) = xi - yj + zk

A:

Q: N g'(x) = Find the derivative of the function g(x) = (3x²5x + 1)e²

A:

Q: Evaluate the following limit using Taylor series. 3tan ¹x-3x+x³ 5 lim x-0

A: Follow the procedure given below.

Q: If f(x) = f'(x) = f'(4) = 4x + 7 2x + 3 find:

A:

Q: For function f(x, y) = 5- | 2 E find the maximum value of the directional derivative at (3, 2).

A:

Q: Sketch the solid region whose volume is given by the iterated integral. (Select the correct graph.)…

A:

Q: Find three positive numbers whose sum is 114 and whose product is a maximum.

A: follow the procedure given below.

Q: The population density of a city is approximated by the model f(x, y) = 2000e-0.01(x² + y²), x² + y²…

A: This is a problem related to double integration. Please follow the general procedure given below.

Q: Suppose that the position of a particle is given by s(t) = 6t³ + 2t +9. (a) Find the velocity at…

A: See the details solution in below

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, and y are positive.…

A:

Q: Sketch the region R of integration and switch the order of integration. 81-x2 LV²²- -10 O -10 f(x,…

A:

Q: Use Newton's method to approximate the indicated root of the equation correct to six decimal places.…

A:

Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

A:

Q: The given family of functions is the general solution of the differential equation on the indicated…

A:

Q: Determine whether the given set of functions is linearly independent on the interval (-∞, co). f₁(x)…

A:

Q: Find all real zeros of the function. f(x) = -5x (1²-16)(x-2) If there is more than one answer,…

A:

Q: Find the integral of So 7x+2x² (x-4)(2x+3X2x+1) dx

A:

Q: 1 3. How many terms of the convergent p-series k=1² must be summed to obtain an approximation that…

A: We have to find no. of terms of the convergent p series.

Q: Evaluate the double integralfor, f(r, e) dA. Sketch the region R. O π/6 8 O sin(0) cos(8) dr de -5…

A:

Q: Determine whether the integral is convergent or divergent. x² V6+x³ [ convergent Ⓒ divergent If it…

A:

Q: 1. Find the area of the region enclosed by the following curves: x₁ = y²2, and x₂ = y. Follow the…

A:

Q: A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of…

A: This is a problem related to differential equation. Please follow the procedure given below.

Q: the Factor Theorem to determine whether x+2 is a factor of P(x) = 2x² + 3x² +4. cifically, evaluate…

A: Here given that x+2 is factor of p(x)  so according to factor theorem x+2 is the factor of p(x) then…