3. If f is continuous and f (x) dx = 8, show that the graph of ƒ intersects the line y = 4 at least once on the interval [1,3].

Q: Find the linearization of f(x) = (1+ x)20 at x = 0. Use it to approximate (1.001)20.

A:

Q: Find a point c satisfying the conclusion of the MVT for the given function and interval: y = ex − x,…

A:

Q: Show that the function f (x, y)=(2 + x-y) / [1+ 2x ^ 2)+(3y ^ 2)] ∈R has a limit at (0,0).

A: I have provided a solution in step2.

Q: Find the linear approximation of the function at the given point. f(x y) = 4x²y3 at (-9,7) O A. L(x,…

A:

Q: Determine two functions, defined on the interval  ( − ∞ , ∞ ) , whose Wronskian is given by  W ( f 1…

A: To determine two functions having the prescribed Wronskian and decide on their linear independence

Q: Find the local maximum and minimum values and saddle point(s) of the function. (DNE if doesn't…

A:

Q: If f"(c)<0, where c is a critical value and f(x) is a continuous function over an open interval I…

A: We have to find f(c)

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function.  F(x) = (1 / x) , a = 2

A:

Q: 8. Find the extremum and saddle points of the function f(r, y) =r' - 3ry + y if any.

A: Due to Bartleby guidelines, only 1st question can be answered if multiple questions have been asked.…

Q: ,is concave up on interval x2-1 The graph of f(x)D OA (-1,1) OB. (0,1) В. Oc. (-1,0) U (1, 0) OD.…

A:

Q: 4. Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e'F…

A: z(x,y) ey F (exy )diff wrt xdzdx = ey F' ex/ye.1/yzx = ey.ex/yyF' (ex/y)and diff wrt ydzdy= ey…

Q: If we use Simpson's rule for a function f(x) = X +1 with n=4 , then the approximate of S f(x)dx is

A:

Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: 10. The line y = 5x – 5 is tangent to the graph of f (x) = (x + k)(x² – x) at the point where x = 1.…

A:

Q: Find the linear approximation to f(x) = at a = 4.

A:

Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: Find the linearization L(x)of the function at a .

A:

Q: Consider the For at function y= In(x+1) . what valves" of x is y undefined ?

A: The given function is y=ln (x+1). The objective is to determine for what values of x is y undefined.…

Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

A: take the partial derivative with respect to x

Q: Find the best linear approximation to f on th e interval [0, 1].                            f (x)…

A:

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = e−2x ,…

A:

Q: 9. If f is continuous and f(x) dx = 14, find f(2x) dx.

A:

Q: is continuous and integral 3 to 1 f(x)dx =8, show that the graph of f intersects the line y=4 at…

A: Given that f is continuous and f13f(x)dx=8 To prove line y=4 intersects the graph of f altleast can…

Q: Find the local linear approximation L (x) of the function f(x) = 5 – x² at =2.

A: To find the linear approximation of given function.

Q: Find the linearization of the function f (x) = x° at z = 1.

A: Given, f(x)=x6

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a =. 3 L(x) =

A:

Q: Show  that the function Z =1/2(eysinx - e-ySin(x) satisfies the La Place’s equation  =0

A:

Q: A governmental agency determines that the Lorentz curves for the distribution of income for dentists…

A:

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

A:

Q: -2 In(x) Consider the function f(x, y) 3y

A:

Q: 9) A function y(x) is increasing and has upward concavity on the interval [-2, 3]. Would a…

A:

Q: find the length of the function over the given interval x=2y, y=-1, to y=1

A:

Q: Find the global minimum of the function f (x) 1 + x² on the interval (0, co0)

A: Given that f(x)= 1+x2.  And we find global minima on the interval (0, infinity).     Here i attached…

Q: Find the linearization L(x) of the function at a. f(x)= sin(x), a= π\4

A:

Q: Find the length of the curve between the specified interval: 3/2 a. y = x7² from x = 1 to x = 4 b. y…

A: (a) Given curve: y=x32 Interval x=1 to x=4 The length of the curve is given by the formula:…

Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

A:

Q: Find the extreme values of the function f at the region of x2 + y² = 4 where: F (x, y) =x² + 2y²-2y…

A: The extrema of the function can be calculated by calculating the derivatives of the function. First…

Q: '18 6. If f is continuous and f(x) dx = 16, find f(2x) dx. %3D

A:

Q: The tangent line to y=f(x) at (7,0) passes through the point (6,−7). Compute the following. a.)…

A: Topic:- calculus

Q: 1. Show that the function x2 – y2 2xy f(x,y) ={ x2 + y? if (x,y) # 0 if (x, y) = 0 is continuous at…

A: If for every ε&gt;0, there exists a δ&gt;0, such that if |x-a|&lt;δ, |y-a|&lt;δ, then the function…

Q: 5. Find the local extreme values of f(x, y) = x²y on the line a +y = 3.

A:

Q: Find the maximum slope on the graph of f(x, y) = 2 sin(ry) at the point P(4, 0).

A: The given question can be solved as shown in step2.

Q: Find the extremum and saddle points of the function f(x, y) = x³ – 3xy + y³ if any.

A: Given problem is :

Q: (2) Is the function f(x) : R → R, sin a 1 ifa # πh,k & Z, ifa = Tk, k ε Z f (x) Borel measurable?

A: Consider the given function, fx=1sinxifx≠πk,k∈Z1ifx=πk,k∈Z   Thus, the given function have infinite…

Q: Which of the following curves have critical points at x=2 and x=-2 * f(x) f(x) = 12 + 4x + 4 x2 – 4x…

A:

Q: 3. If f(x) = (1–- t²)e*dt, on what interval is the curve y =f(x) upward? concave

A:

Q: 以く2 g(x) = X = 2 *一2 h continuous at MArDl (0,2]

A: The given function is: g(x)=x2+1, x&lt;25        ,x=21x-2,x&gt;2

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.