Find a zero of f(x) = e*-2x 1. Is this a contraction or not? Justify your answer.

Q: Find the linearization L(x) of the function at a. 9 f(x) = a = 3 - L(x) =

A: We have to find the linearization L(x) of the function at a.  We have, f(x)=9x and a = 3

Q: Verify Rolle's theorem for f(x) = x* – 4x+8 over the interval [0, 2].

A:

Q: Find aa and bb so that the function f(x)={4x^3-3x^2+5, x<-2         {ax+b,             x is…

A:

Q: At waht x does f(x) have a local(relative) maximum?

A: A function f(x) is defined for x values there are local maxima and local minima in the given curve.

Q: ,x 1 Is the function k(x) = {x²-1 2,x = 1 continuous at x = 1?

A: We use L' hospital rule to find the limit.

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x ln…

A: Now differentiating with respect to x, we get

Q: The function y = 1/x does not take on either a maximum or a minimum on the interval 0 < x < 1…

A: Extreme Value Theorem:If a function f(x) is continuous on a closed interval [a,b], then f(x) has…

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: Let X2=mY , where 'm' belongs to set of integers. And here we have taken a parabolic path .

Q: Find linearization L(x) of f (x) = Vx at a =4 and use to approximate 7.8.

A:

Q: Consider the function f(x) = 648x¬² + x³. Taking the initial point as x = 6 and increment value as…

A: Here, fx=648x2+x3 Take x0=6 and △=1 Iteration 1) k=0 of xk Now, xk+1=xk+2k△ Here, x0=6…

Q: I. Is the function given by g(x)=x²-3x + 2 continuous over the interval (-4, 4)? Why or why not?

A: Function given is- g(x)=x2-3x+2 continuous over the interval (-4,4) . Wee need to determine whether…

Q: Show that the function f(x) = e1/2)[(x-µ)/a}° has a relative maximum at x = µ.

A: fx=e-12x-μσ2 Differentiating with respect to x, we get…

Q: 5. Prove f(x) = e* + x has a root on the interval (-1,0) using the Intermediate Value Theorem.

A:

Q: Let f be a continuous function with f'(x) = 3x² Of has no relative maxima. 0x=0 0x=2 0x=1 - 6x. At…

A: f be a continuous function with f'x=3x2-6x

Q: What is the local linearization of f(x) = near x = 1? NOTE: Enter your formula exactly, or round…

A:

Q: Find the values of k that make the function continuous. Jk² + 18x, x > -3 f (x) = kx, x < -3

A:

Q: find the critical point and classify the function f(x,y)= x3 +y3 - 6xy

A:

Q: 1 Differentiate f(x) = log, x from the first principle. Note: f'(x) = x In a

A: q- differentiate the function fx=logax from the first principle it is known that, according to first…

Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: Find the absolute maximum value of f(x) = x2 – 2x + 10 over the interval 0, 3 -

A: Find your answer below

Q: 95. Prove that the average rate of change of the linear function f(x) = −2x + 4 on any interval I is…

A: The average rate of change of a function f(x) over an interval [a,b] is given by f(b)-f(a)b-a. It is…

Q: Find the linearization of f(x)=ln(x2-3) at suitably chosen integer near X=2.1. Then use the…

A:

Q: FIND a) F(5) b)interval over which F(x) is decreasing  c) what x=? Where F(x) has a maximum value

A: Given, F(x)=∫0xf(t)dt Graph,

Q: How do you evaluate the limit as t approaches 0 (1/t*the square root of 1 + t  - 1/t) with the…

A: Obtain the value of limit as follows.

Q: Use the e - S definition to show that the function x- 1 f(x) = x +2 %3D is continuous at x = 3.

A:

Q: Integrate f(x) from x = 0 to 10 using Three-Point Gauss-Legendre Quadrature. f(x) = 5000+24563x -…

A: Given f(x)=5000+24563x-7418x2+768x3-31x4+0.14x5 Let I=∫010f(x)dx Here a=0 and b=10

Q: What is local linear approximation for f(x)= e*" -6* near x = 0? Note: Must show answer is equal to…

A: Hey, since there are multiple subpart posted, we will answer the first question. If you want any…

Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

A:

Q: Find the absolute maximum and absolute minimum of the function on the given interval. f(x) = x – In…

A:

Q: (a) find the local linearization of f(x)=fourth root(x) at x=16 (b) Use the linearization to…

A: It is a linear approximation problem

Q: Find the local maximum value of f using both the First and Second Derivative Tests. f(x) = x + V1 -…

A: First calculate critical point at which either local maxima or local minima will occur by putting…

Q: What is the maximum point of the function f (x) = x² - x on the o terval [-2,2]?

A:

Q: . Find the maximum value of f(x) = In(x – In x) on the interval -sxs. Show all steps .

A:

Q: Find the value of the constant c such that the function f(x)= (x-2)/( (root 4x+1)-3) if x#2, c if…

A: And

Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

Q: Find the absolute maximum of f(x) = x³ – 12x + 1 on the interval [0, 4]. -

A:

Q: Suppose that t hours after the injection of x milligrams of adrenalin the response is R units, and…

A: The response after t hours of x mg of adrenalin is R=te-t(c-x)x where c is any constant. We want…

Q: find the absolute maximum and absolute minimum values of ƒ over the interval ƒ(x) = x - 2 ln x,…

A: The given function and the interval is,

Q: A once-popular dog’s chew toy is slowly declining in popularity. The quartic function…

A: Given that x is the number of years since 1993 So 2001 means x=2001-1993=8

Q: What is the domain of g(x)=ln(25x-x^2) Show all the work.

A:

Q: If 7x-5,x < 1 h(x) 3x2 – x, 1 < x < 3 Is h(x) continuous at (x=1)?

A: Given: hx=7x-5,x&lt;13x2-x,1&lt;x≤3 We know that any given functiony=fx will be continuous at x=a…

Q: : Find the value of k that makes function continuous at x = 4 %3D 3x + 6 x > 4 f(x) = 6x – k x < 4 -

A: To find: The value of k

Q: Consider the functions f(x, y) = x2 − y2 and g(x, y) = x2 + y2 .                             (a)…

A: Given functions are f(x,y)=x2-y2  and g(x,y)=x2+y2.

Q: Consider the function f(x) = x - 3 ln(x) on the interval The absolute maximum value is and this…

A: Consider the given function, fx=x-3lnx differentiate the function with respect to x,…

Q: Find the absolute maximum value on (0, oo) for f(x)37-4x--

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: If F(X) is an antiderivative of *-2 + x-', then what is the value of F(1) - F(-1)?

A:

Q: Is the function F(x) as given is constant, increasing, or decreasing on the interval (0, ∞)?…

A: Fx=∫x2x1t dt⇒Fx=lntx2x⇒Fx=ln2x-lnx⇒Fx=ln2xx          ∵lnx-lny=lnxy⇒Fx=ln2

Q: Estimate v16.3 using the linearization L(x) of f(x) = /x at a = 16. (Use decimal notation. Give your…

A:

Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

A:

Q: Find Tn cebtered at x=0 fir akk b for the function f(x) = 1/(1+x) at a=0

A:

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.