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Math
CalculusFinite Mathematics and Applied Calculus (MindTap Course List)7th Edition

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Chapter 11.5, Problem 67E
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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 67-72, find the equation of the straight line described. Use graphing technology to check your answers by plotting the given curve together with the tangent line.

Tangent to y = e x log 2 x at the point ( 1 , 0 )

To determine

To calculate: The equation of the tangent to the graph of the function y=exlog2x at the point (1,0). Also, sketch the curve along with the tangent line.

Explanation

Given Information:

The provided function is y=exlog2x and the point is (1,0).

Formula used:

The derivative of e raised to a function is ddxeu=eududx.

The derivative of the log to base b of x is ddxlogbx=1xlnb.

Constant multiple rule of derivative of function f(x) is f'(cx)=cf'(x) where c is constant.

Calculation:

Consider the function, y=exlog2x

Find the slope of tangent line to the function xyāˆ’y2=x2āˆ’3 by determining the derivative.

Then, the derivative of the functions is,

dydx=ddx(exlog2x)

Apply the product rule of derivative,

dydx=ddxexā‹…log2x+exā‹…ddx(log2x)

The derivative of the log to base b of x is ddxlogbx=1xlnb.

The derivative of e raised to x is ddxex=ex.

Now, apply the above formula and simplify the derivative,

dydx=exā‹…log2x+exā‹…1xln2=exlog2x+exln2

So, the slope of the tangent to the graph of function y=exlog2x is exlog2x+exln2.

Now, the slope at the point (x1,y1) is evaluated by calculating the value of dydx|(x1,y1).

Here, x1=1 and y1=0

Then, the slope at the point (1,0) is,

dydx|(1,0)=e0log2(0)+e1ln2=1ā‹…0+eln2=eln2

Thus, the slope of function y=exlog2x at the point (1,0) is eln2

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Elementary Geometry For College Students, 7e

Subtract: 60,0004,803

Elementary Technical Mathematics

Completing the Square In Exercises 35-42, Find or evaluate the integral by completing the square. 2x2+4xdx

Calculus: Early Transcendental Functions (MindTap Course List)

Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote....

Single Variable Calculus: Early Transcendentals

Finding a Maclaurin Polynomial In Exercises 17-26, find the n th Maclaurin polynomial for the function. f(x)=si...

Calculus of a Single Variable

16. (This is additive version of Exercise 37 in Section 4.6, with proofs the same except for notation.) Let and...

Elements Of Modern Algebra

Geometry: Characteristics of a Cube The object shown in Figure 27 is a cube (all edges are equal in length). Us...

Trigonometry (MindTap Course List)

The solution to dydt=ky, where k is a constant and P0 is the value of y when t = 0, is a) y = ekt b) y = xekt c...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

is the binomial series for:

Study Guide for Stewart's Multivariable Calculus, 8th

Data from a survey of a representative sample was used to estimate that 32% of computer users in 2011 had tried...

Introduction To Statistics And Data Analysis

In Exercises 116, determine whether the argument is valid. pqrqpqpr

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 41 to 50, use deduction to state a conclusion, if possible. If you study hard and hire a tutor, th...

Elementary Geometry for College Students

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