Consider the following function x² - 2x, if x < 0, f(x)= = -2x, if x > 0. 1. Show that f(x) is continuous at x = 0. 2. Use the limit definition of the derivative to compute f'(0). Hint: You will need to use directional limits.

Consider the following function x² - 2x, if x < 0, f(x)= = -2x, if x > 0. 1. Show that f(x) is continuous at x = 0. 2. Use the limit definition of the derivative to compute f'(0). Hint: You will need to use directional limits.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

See similar textbooks

Related questions

Q: PLs help asap on all asked parts pls

A: Step 1: Understand the ProblemWe need to find the equations of the tangent lines to the curve y=x2…

Q: Show work on each step , help solve the problem in picture pls

Q: Use technology to find f'(2), f'(15), f'(-3) for the given function when the derivative exists. f(x)…

A: Step 1: Step 2: Step 3: Step 4:

Q: Solve the initial value problem

A: First of all, We will simply integrate both sides of given initial value problem (IVP) .Then,We will…

Q: assumed that c is a constant such that c > 1. f(x) = In (4x) g(x) = 6 sin (9x) Red Cord: f'(c) Green…

A: Step 1: Step 2: Step 3: Step 4:

Q: The regular selling price of a new kitchen aide mixer is $250. a store is offering a pre-black…

A: The given values in the problem are:Regular selling price of the mixer (P) = $250Discount rate (d) =…

Q: a direction field is drawn for the given equation. Sketch some integral curves.

A: To sketch the integral curves:Start at any point: Pick a point on the grid, such as (1,0), (2,0),…

Q: Find all local maximum and minimum points of ƒ = 2x² − xy + y² − 5x + 6y – 9.

Q: 3. For the set of simultaneous equations: a. Form the augmented coefficient matrix b. Solve the…

Q: explain in full detial

A: Step 1: Step 2: Step 3: Step 4:

Q: MAA MATHEMATICAL ASSOCIATION OF AMERICA WeBWorK/2024-FALL-MATH1007-SECTION-C / Assignment 2 / 2…

A: Step 1: Step 2: Step 3: Step 4:

Q: Solve problem in picture, show work pls :) if you can break it down and explain your process to me…

A: Step 1:Step 2: Step 3: Step 4:

Q: QUESTION 3 Evaluate the integral. 3 cost 5x dx ○ 9 X 2x + 2/10 sin 5x + 3 sin 10x + C 160 O 9 3 X +…

A: If you have any problem let me know in comment box thankyou.

Q: Find the average height of the paraboliod z = x² + y² over the square 0 ≤ x ≤ 3; 0 ≤ y ≤ 3.

Q: Verify that the function is a solution of the initial value problem.

Q: The material for the bottom of an aquarium costs half as much as the high strength glass for the…

A: The required optimization problem is solved using Lagrange multiplier as follows:Step 1: Step 2:…

Q: Hello, I need help I have no clue how to do 2.5 Trig derivatives my teacher went over the topic…

A: Before we start, it's important to understand the basic rules of differentiation. The derivative of…

Q: The question and the solution are in the attached photo could you please explain the solution

Q: determine which equations are exact and solve them.

A: Step 1:Step 2: Step 3: Step 4:

Q: 10. Find (ƒ-g)(x) where f(x) = 2x², g(x)=(x+1)². (f-g)(x) = x²-2x-1 (f-g)(x)=3x²+2x+1 ○ (ƒ-g)(x) =…

A: Step 1: Given two functions f and g with a common domain, the function f−g can be defined as…

Q: hello, i don't understand because i got a lot of different numbers each time. like 6 and 10 or 2 and…

A: The problem is asking us to find the values of parameters a and b that make the function f(x)…

Q: Carbon-14 is a radioactive substance that decays over time. It is used to date fossils and other…

Q: Find the cross product axb a= (5,7,2), b= (-7,3,-3)

A: Step 1: Identify the formula for the cross product (ex: a x b) of two vectorslet:a and b be vectors…

Q: Please write explanations for each step

Q: Solve and show work

A: Here is the step-by-step explanation:Part (a): Mass of the Rod:The mass of the rod can be found by…

Q: 1. The velocity of a particle after t seconds is given by v(t) = meters per second. If the initial…

Q: The graph of a function f is shown. y 800 400 x 0 20 40 60 (a) Find the average rate of change of f…

A: a. First find f(50) and f(60).f(50)= 400f(60) = 700Now use the AROC…

Q: 1

A: Let us address the questions based on the graph provided. a) limx→1+f(x)From the graph, as x…

Q: 1x-41 2. Consider the following function: f(x) = 12-16 Compute the following limits, if they exist.…

Q: Use limits to show that the function f (x) = x2 + 3 for x < 1 10 − x for 1 ≤ x ≤ 2 6x + x2 for x…

A: We determine whether the function f(x) is continuous at x = 1 and x = 2. We need to use the…

Q: When a bacteria colony reaches 150 thousand, it is treated with antibiotics. After 2 weeks, the…

A: Given the exponential model B(t)=B0⁢ekt, where B(t) is the bacteria population after t weeks, B0 is…

Q: For each limit, verify that the function is continuous on its domain, then use direct substitution…

A: To solve the limits, we will first check the continuity of the functions at the given points, and…

Q: Give the appropriate form of the partial fraction decomposition. v+3 12²(y+1) v+

Q: a. Starting at (x,y)=(1,1), find a unit vector u=⟨a,b⟩ that points in the direction of the point…

A: a. Finding a unit vector u=⟨a,b⟩ that points in the direction of the point (3,4) starting at (1,1):…

Q: 4. Consider the nonlinear ODE with initial condition x' (t) + ex(t) = sint, t€ (-∞, ∞0), x (0) = 0.…

A: //The answer above is a possible detailed explanation of the question mentioned and…

Q: Solve show work/steps

A: Step 1: The area can be solved as follows:

Q: 9. Expand (multiply out) the expression: (4 + 2x)³. Show your work. Combine like terms in your final…

Q: don't be lazy please. dont use chatgpt. Actually explain it out in good detial

Q: Let f and g be any two functions, and let M and N be non-negative real numbers. Determine whether…

Q: Help me with the product rule, Differentiate each function with respect to x.

A: There are two different ways in which we can use product rule of differentiation.We will see both…

Q: √√5 - 2x² ≤ f(x) ≤ √√5 − x² - for −1 ≤ x ≤ 1, find 63. If √5 lim f(x). 0-x

A: We are given two functions that bound f(x):5-2x2≤f(x)≤5-x2for x in the range -1 to 1.

Q: Profit Function for Producing Thermometers The Mexican subsidiary of ThermoMaster manufactures an…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find two power series solutions of the given differential equation about the ordinary point x = y" +…

A: To solve the given second-order differential equation using power series, we first rewrite the…

Q: Explain in full detial, the idea of Bernoulli's Equation, and clear handwrititng

Q: Find the particular solution of the differential equation: - 02 fy = 4 when x=1 ○ (E) Оу oy = 200…

A: Step 1: Step 2: Step 3: Step 4:

Q: ← 8:16 PM 1 Question 18 ▾ > > 7.21 4G K/S 4G 70 For this exercise, consider the polynomial shown…

A: Step 1:Step 2:

Q: This question came from a review packet that was handed out in means of us studying for our first…

Q: it is possible for ben's weight to be 200% more than his brother's weight

A: The question is asking if it's possible for Ben's weight to be 200% more than his brother's weight.…

Q: 1) For the following set of simultaneous equations: a) form the augmented coefficient matrix b)…

A: Given: 2x + y + z = 8 7x+y+3z = 20 5x - 3y+2z = 3 a. Form the augmented coefficient…

Q: Find the direction cosines of vector (4, -8,-8)

A: The direction cosines of a vector are the cosines of the angles that the vector makes with the…

Question

pleasde help thank you

Consider the following function
x² - 2x,
if x < 0,
f(x)=
=
-2x,
if x > 0.
1. Show that f(x) is continuous at x = 0.
2. Use the limit definition of the derivative to compute f'(0). Hint: You will need to use directional limits.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here