Tangent Line. If p(x) = 2x+ 6x + +2, (a) Then p'(1) = !! (b) The equation of the tangent line to the function p(x) at x = 1 is %3D

Q: 3. Approximate the first order derivative of f(x)= x² + 2x at x = 3, using Forward, Backward and…

A: Formulas for differences are enclosed next page

Q: Directions: In implicit differentiation, we differentiate each side of an equatiom wariables…

A: Topic:- function and it's Derivatives

Q: Find an equation for the tangent line to the graph of the given function at (-3,1). f(x) = x² – 8…

A: Given: The function fx=x2-8and the point -3,1. To find: The equation of tangent line to the graph of…

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Q: Ordinary Differential equation is an equation which involves * One derivative two derivative O Non…

A: an ordinary differential equation is a differential equation containing one or more functions of one…

Q: tionship between x and y.

A: Linear Eq: 9.x=1,2,3,4,5y=f(x)=2,4,6,8,102y=xSo, this is the requiredequation of line.

Q: 5y + xy-

A: Differentiation: 5y+xy-4=0 ddx(uv)=udvdx+vdudx ddx(y)=dydx

Q: Find an equation of the tangent line to the graph of the given function at the specified point. f(x)…

A: Consider the given function. fx=5excos x

Q: X- 1 Find the anti-derivative of /1-x² 1- x2 – Arcsin x + C V1- x² - Arcsin x + C 2 2/1- x2 - Arcsin…

A: Here we have to find the antiderivative of x-11-x2 ⇒I=∫x-11-x2dx

Q: (x2-1) (x²+1-x) Q4 / Find the equation of tangent line at x = 1, where f(x) x*-x3

A: A tangent line to curve is a line that just touches the curve only one point.

Q: Find the equation of the line tangent to the graph of y = 4 ln(x) at a = 2. Enter exact values.…

A: detailed solution is given below

Q: Tangent line of a graph of f(x)=x(b^x)at x=1 is equal to the tangent line for the graph of…

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Here, we are going to solve only one question and for the remaining question please post the…

Q: Identify the equation of the tangent line of the function: f(x) = 3x at x=2

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Q: V3x-e2x-(x ln x)(ln(ln x))| In(ln x) Given a function, y = dy Show that dx V3x-e2x (x In…

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Q: se LONG METHOD DERIVATIVES to find the slope of the tangent line to the curve: (x) = -2x 1 at point…

A: Topic:- calculus and geometry

Q: y=sin-1(x/x^2-1)x=3^1/2 find the equation of the tangent line

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Q: (3) A wire 10 cm long is cut into two pieces, one of length x and the other of length 10 - x. Each…

A: Length of wire = 10 cm

Q: cosh x sinh x dx 2 (cosh x + 3)

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Q: equation of tangent line of f(x)=5x^3+1 at x=1 is * O y=15(x-1) O y=15 x-9

A: Given: The function f(x)=5x3+1 and a point x=1

Q: Find an equation of the tangent line to the curve at the given point. y = ln(x2 − 3x + 1),    (3,…

A: Given equation of curve y = ln(x2-3x+1)

Q: 12. The Definition of the Derivative Find the formula for the instantaneous rate of change of f(x) =…

A: Given:

Q: 6. (10 points) Give the equation of the tangent line of the following function at point a = 1: xe…

A: Solve by Differentiation

Q: True of False: Derivative of (arctan(e^(-x^2))) = [-2xe^(-x^2)] / [1 + e^(-2x^2)] Show your…

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Q: Find the differential equation of the family of curves. (can you show the step-by-step solution) 2.…

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Q: Find an equation for the tangent line to the graph of the given function at (-2,3). f(x) =x - 1 Find…

A: Topic:- application of derivatives

Q: Find an equation of the tangent line at the given point.  f(x)=3/x2  , at x= -1

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Q: Find an equation for the tangent line to the graph of the given function at (-5,29). f(x)=x² +4 Find…

A: f(x)=x^2+4   (-5,29) slope=m=dy/dx m=dy/dx=d(x^2+4)dx=2x m=2x (-5,29) m=2(-5)=-10

Q: sin x 1) lim- 2) If f (x)=x +1 then the equation of tangent at x-2 is y-4x-3. d 3) dx -2 2

A: find limit using L hospital Rule    Since you have posted a question with multiple sub-parts, we…

Q: Find an equation for the tangent line to the graph of the given function at (-3,6). f(x) = x2 - 3…

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Q: 27 SECOND DERIVATIVES Find TUTORIAL 22 if y-In (x + 1). Answer 2-2x² 22-2

A: Note:-As per your mentioned request I am solving question 1 from the given picture. Given is…

Q: Vx-1 lim x-1 x-1 3 Question 6- Find the equation of the tangent line to y = - at the point where…

A: On solving first 3 question we will get

Q: Find an equation for the tangent line to the graph of the given function at (- 3,13). f(x) = x² + 4…

A: From the given problem:   fx=x2+4px1,y1=-3,13   The expression for the slope of the tangent to the…

Q: 2 *sinh“ x – sinh x+ cosh x dr -dx cosh¯ x

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Q: Find an equation of the tangent line to the curve at the given point. y = ln(x2 − 3x + 1),      (3,…

A: To Find an equation of the tangent line to the curve at the given point. y = ln(x2 − 3x + 1),…

Q: HIGHER DERIVATIVE OF A FUNCTION AT A POINT 1. If y = 3x3 – 6x2 + 6x + 1, find d dy dx ' dx2 at x = 2

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Q: 3. f(x) = 6xi – 3x ; x € [- 2,1 first derivative critical numbers stationary points End Points…

A: Here, the given function is: f(x)=6x53-3x23; x∈-2,14

Q: Finding an equation of tangent line to the graph ln(xy) - x2+y2=0 at (1,1)

A: To find equation of tangent line to the graph of below curve at (1,1).

Q: sinh x – cosh x + ecothx dx - sinh2x

A: Let's find.

Q: A curve has an equation x2- 6x + 2y - 8 = 0. Find the equation of tangent and normal line at x = 3…

A: Given the Equation of the curve : x2-6x+2y-8=0 ⇒2y=-x2+6x+8⇒y=12(-x2+6x+8) ⇒f(x)=12(-x2+6x+8)…

Q: (a) Use a graphing utility to graph the slope field for the differential equation. 20- 20 y(x) 10-…

A: The slope field is the graphical representation of a differential equation. From a slope field, one…

Q: 4. у"- Зу' + 2у cos e*

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Q: 2. 1950, a seed was planted same as the year as Jilian was born. When she celebrated her debut, the…

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Q: Equation of the line tangent to the graph of f(x)=(x)(1-2x)^3 at (-1,1).

A: The given function is: f(x)=(x)(1-2x)3 And, at point (1,-1), we have to find the equation of the…

Q: 7. A differential equation is an equation which contains at least one derivative on it. *

A: A differential equation contains

Q: A differential equation is an equation A that contains a derivative like y'(x) as well as the…

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Q: Partial Differentiation a2z 1. If z = e* sin y + e³ cos x, verify a²z = 0 ду?

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Q: sinh (2.Inx) n(coshx+Sinhx)+in(cashx-sinh x).

A: We have to rewrite the given expression by using the exponents.