Exercise 4 Consider the function f that is def ined over R as: f(x)=x²– 3r² + 4x. Denote by (C) its representative curve in an orthonormal sy stem. 1) Calculate lim f(x) and lim f (x). 2) Calculate f"(x), then set up the table of variations of f. 3) Let (T) be the tangent to the curve (C) at a point of abscissa 1. a- Determine an equation of the straight line (T). b- Study the relative positions of the curve (C) and its tangent (T) accordina to the values of x. 4) Draw the curve (C) and the straight line (T).

Exercise 4 Consider the function f that is def ined over R as: f(x)=x²– 3r² + 4x. Denote by (C) its representative curve in an orthonormal sy stem. 1) Calculate lim f(x) and lim f (x). 2) Calculate f"(x), then set up the table of variations of f. 3) Let (T) be the tangent to the curve (C) at a point of abscissa 1. a- Determine an equation of the straight line (T). b- Study the relative positions of the curve (C) and its tangent (T) accordina to the values of x. 4) Draw the curve (C) and the straight line (T).

Name: 2 Exercise 4Consider the function f that is def ined over R as: f(x) =
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 2 Exercise 4Consider the function f that is def ined over R as: f(x) =x'– 3r² +4x.Denote by (C) its representative curve in an orthonormal system.1) Calculate lim f(x) and lim f (x).2) Calculate f"(x), then set up the table of variations of f.3) Let

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

(The Second Derivative Test) Let f : [a, b] → R be differentiable on (a, b). Suppose c ∈ (a, b) is such that f '(c) = 0, and f ''(c) exists. (a) If f ''(c) > 0, prove that f has a local minimum at c. (b) If f ''(c) < 0, prove that f has a local maximum at c. (c) Show, using two specific examples, that no conclusion can be made if f ''(c) = 0.
Dete‎rmine if f (x, y) = ={(xsi‎n3y)/(x‎2+y6), (x, ‎y) ≠ (0, ‎0) ={1, (x, y) = (0, 0) is‎ co‎ntinuous at (0,‎ 0)
let f be a function with f(0)=1 and f(x)=cos(x2) a) find the linearization of f at x=0 b) estimate the falue of f at x=0.1 c) do you think the actual value of f at x=0.1 is greater or less than the estimate in part b? explain
Find the degree of homogeneity of the function F(x, y) = x y/ x + y. Hence show that Euler′s Theorem holds?
Examine the continuity on the set R2 , determine the set on which the function is differentiable and determine the first-order partial derivatives of the function
Examine the continuity of f(x,y) at the origin, where a) F(x,y) = ( 3yx^2/y^2+2x4) , x,y!=0,0 =0, x,y=0,0 b) If x increases at a rate of 6cm/sec at the instant x=5cm and y=2cm, at what rate y must be changing inorder that the function 3xy-2xy^2 shall be neither increasing nor decreasing
How do we find the linearization of g(x, y) = tan−1(xy2) at the point (1, 1). and use linearization to estimate g(1.08, 1.037). thank you.
15) Annual U.S. imports from a certain country in the years 1996 through 2005 could be approximated by I(t) = t2 + 3.5t + 48 (1 ≤ t ≤ 9) billion dollars, where t represents time in years since 1995. Annual U.S. exports to the country in the same years could be approximated by E(t) = 0.5t2 − 1.4t + 13 (0 ≤ t ≤ 10) billion dollars. Assuming that the trends shown in the above models continue indefinitely, calculate the limits lim t→+∞ I(t) and lim t→+∞ I(t)/E(t) algebraically. (If an answer does not exist, enter DNE.) lim t→+∞ I(t) = lim t→+∞ I(t) E(t) = Interpret your answers. In the long term, U.S. imports from the other country will (select) (be rounded or rise without bound) and be times U.S. exports to the other country. Could the given models be extrapolated far into the future? Yes or No
Assume the second derivatives of ƒ are continuous throughout the xy-plane and ƒx(0, 0) = ƒy(0, 0) = 0. Use the given information and the Second Derivative Test to determine whether ƒ has a local minimum, a local maximum, or a saddle point at (0, 0), or state that the test is inconclusive. ƒxx(0, 0) = -6, ƒyy(0, 0) = -3, and ƒxy(0, 0) = 4
4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard theorem for a suitable domain D. b. Then estimate the interval of existence of the solution.
Let g(u) be a differentiable function, and let f(x, y) = g(x^2,y^2) Find the direction of maximal increase of f at the point (1, 1) in termsof g'
Consider the functiona. Decide if f is continuous at (0,0)b. Decide if is differentiable at (0,0)c. Can the partial derivatives f be continuous at (0,0)?