Let I = f(x) dx, where f is the function whose graph is shown. y f 6. 1 4 (a) Use the graph to find L2, R2 and M2. L2 R2 M2 %D 3. 3. I| ||

Q: The surface area of a balloon can be represented by the function S(r) = 4xr², where r is the radius…

A: The surface area of the balloon can be represented by S(r) = 4πr2 Radius of the balloon increases…

Q: 1 Find the range of the function y =x+ 3 when the domain is: a (-1, 0, 1, 2} b {x: -1 Sx S 2} c R

A:

Q: 3. Use the function g(x) = 2x- 3 to fill in the table below and graph. %3D a) What type of function…

A: Domain set of all input values where f defined Range set of all output values

Q: Q4) f(x, y) = x"/s –x/ay² Does the function is harmonic ?

A: If a function satisfied Laplace equation then the function is called harmonic function

Q: Q2\\ Find the value of (a) that make the function below continuous at x 2: (a*x-2a x22 fx) = 12 x<2

A: Definition used-                     Continuity of function -                     A…

Q: A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of…

A:

Q: For the function f (x) = a-5a2. (a) Evaluate the average rate of change from r = -2 to r 1 (b) What…

A: Given, The function fx=x3-5x2 We have to solve for part a and b

Q: Q6: Find the local extreme values of the function: f(x, y) = x2 + y² – 6y + 5

A:

Q: 2. The graph of f(x) which is a straight line is shown in the figure to the (b,10) b+l S(x) right.…

A:

Q: What is the average rate of change of the function f(t) = t² - 7t between t = and t = -4? -10 -14…

A:

Q: 3. When is the function increasing and when is it decreasing? f(z) = re==z3)? xe 2 f(x)=xe 4X2)

A: Solution:

Q: Use the chemical reaction model with a given general solution of y=. y = 95 grams when t = 0; y = 14…

A: The function f(t) is a rule that associates or fixes a number to the particular point t. A…

Q: c) In which unit direction does the graph of z=f(x, y) have its steepest decline at the point (2,3),…

A:

Q: For the function f(x)=x^2 e^−2x, find:    (a) the local and absolute extrema.    (b) the…

A:

Q: The surface area S (in square meters) of a hot-air balloon is given by S(r) = 4xr where r is the…

A: If f is a function of x and x is a function of t, then ft is nothing but the composite function fxt.…

Q: gc)= Where is gux) increasing where is gixJ decreasing.

A: Given function: gx=x2-12x2-4x+3 The function is increasing in an interval where f'x&gt;0 The…

Q: d*y 4. Find 5 of the function f (x) = - e dz"

A:

Q: Find the point P on the graph of the function y Vĩ closest to the point (11, 0) The x coordinate of…

A: Solved below

Q: df If f is the linear function f = 5x – 9, what is the value of dx

A: The given function is f=5x-9

Q: The graph of y = f(x) is given below: 3 2 -3 - –1 2 3 4 5 6 7 (x)dx = 4.5, then f(x)dx =

A:

Q: dr a) -sin³ x b) sin² x Q7. Find the range of the function y= a) x>0 b) x 3

A:

Q: For some positive constant C, a patient's temperature change, T, due to a dose, D, of a drug is…

A: To find the solution

Q: 9 Given the graph to the right, find f(x)dx. ff(x)dx. 3 10- 8- 6- 4- 2- 0 2 4 6 -8 10 X

A:

Q: df-1 For the function y = f(x)=x²-x-1, x ≥ 0.5, find dy (ƒ-¹) '(1) = y=

A:

Q: df-1| For the function y = f(x) = x + 3x + 1, > 1.5, find dy (f-)'(3) = %3D

A:

Q: Find the average rate of change of f(x) = 9x² – 3 on the interval [2, t]. Your answer will be an…

A: Use formula of avg rate of change

Q: Consider the function f (x, y) = 7x² + 6xy + 5y² + 7x Draw the graph of f(x,y). Your graph should…

A:

Q: Find the average rate of change of f(x) = 6x² Your answer will be an expression involving t. 3 on…

A: The given function is f(x)=6x2-3 We have to find the average rate of change of the function on the…

Q: Q4) r(x, y) = xs -x/ay2 Does the function is harmonic

A: We know that a function in two variable is called harmonic if it satisfies the Laplace equation…

Q: %3D 42. Find f(x) dx for each graph of y = f(x). (a) y. (b) y 2. 1. 3 aronh of flr) = 2x + 3 and

A: Given query is to find the valuebof intgy from the graph.

Q: d²y 2. Determine of the function y = dx2 x²cos (x)

A:

Q: c) value of x as t→ 00. Find the proportion of the population that escapes the epidemic by finding…

A: We have to find the proportion of the population that escapes the epidemic by finding the limiting…

Q: f(x)=-2x^2+11x+16/e^x (i) Make the standard analysis of the function f(x), that is: (ii) Use (i)…

A: the given function is f(x)=-2x2+11x+16ex the domain of the function is -∞,∞ the function has no…

Q: For the function y = f(x)- T 2. I- + 3, a 2 0.5, find df-1 (f-')'(4) = Preview

A:

Q: Draw the graph of f(x)=2-|x|, and use it to find the value of (2–|æ|) dx . -2 Write your answer as…

A:

Q: A startup business projects its instantaneous rate of revenue flow to be given by R(x)=120,000e^.03t…

A:

Q: Q6: Find the local extreme values of the function: f(x,y) x2 + y? - 6y +5

A: Given the function f(x,y)=x2+y2−6y+5

Q: Find the point of diminishing returns (x.y) for the function R(x), where R(x) represents revenue (in…

A:

Q: Q4:Find the relative extrema of f (x) I+3 I- 2

A:

Q: What is the range of the function y = 8cos(x-30°) –2? (A) {y]y e R} (B) {yl-2 sys 8,y e R} (C)…

A:

Q: er the function f(x) = (x +1)( x-1)2, At what value of x will the graph of f cross the y-axis ?

A:

Q: Use the graph of y = f(x) to graph the function g(x) = 2f(x- 1) + 1. y- f(x) AY

A:

Q: Consider the function: g(x) = 2x + 6x 2 Find the average rate of change of g(x) between the points =…

A: We will Use the average rate of change formula to solve our given problem.

Q: A spherical balloon with radius inches has volumeV(r) =4/3 π r2. Find a function that represents the…

A: Given that, A spherical balloon with radius inches has volume V(r) =4/3 π r2 We have to find a…

Q: Q3) State the approximation for a differentiable function f(x): (a) V51 (b) V123 (c) (33)

A: (a) 51 Linear approximation is obtained as Lx=fa+f'ax-a Consider the function fa=a. On…

Q: The function D(p) gives the number of items that will be demanded when the price is p. The…

A:

Q: Let l=∫4 0 f(x) dx where f is the function whose graph is shown. (a) Use the graph to find L2 ,R2 ,…

A: Given:  Let l=∫4 0 f(x) dx where f is the function whose graph is shown. (a) Use the graph to find…

Q: y? For function f (x, y) x2+1 Starting from the point (1, 2), at which direction does the above…

A:

Q: Find the inflection point(s) of the function  f(x) = 5e−(x^(2))

A: