Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
calculate slope of tangent f(x) = sqrt2x+3  where x=2 use this method  show all steps and calculations

calculate slope of tangent f(x) = sqrt2x+3  where x=2 use this method  show all steps and calculations

Advanced Engineering Mathematics
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
icon
Related questions
Question

calculate slope of tangent f(x) = sqrt2x+3  where x=2

use this method 

show all steps and calculations

Ex. 2 Find the slope of the tangent to y=-x²+2x+6 for the point when x=5 @x= 5+h y=(3+h)² + 2(5+h) +6 -25-10h-h² +10-2h+6 =-9-8h-h² (5th, -9-8h-1²) =lim X (-8-h), h+0 100 -8-h Find 'y' coordinate @ y = -(3) ² + 2(5) + 6 = -25+10+6 --9 : the point is (5,-9) meon= Rim f(sth)-f(s) 5th-3 h+o = fim - 9-8h-h² - (-a) ho 3th-3 -8h-h² - Rim Ex 3. Determine the slope of the tangent to f(x)- OP (3,4) X = 3+h f(31h)= 3+ha9 31h = 12+h 3+h .: the slope of the tangent at paint Pis -1, hvo x=51h f(son) (Sthis = √9th : the slope of the tangent at 4-5 is thro Mion" 2+9 at P(3,4) X nº fim +(3+h)-f(3) 3+h-3 12th -U =-8, hvo = Rum ho Ex 4. Find the slope of the tangent to f(x)=√x+4 atx=5 fls) = (344 = lim 2+0 lim hao = lim em hinh ma h (12th ~ - 4 (3+h) ) = =h 3th + 12th-12-4h. 3+h h - emm 9-1-9 nno mtan= lim f(s+h)-f(3) 5th-5 Tain -3. -3 31h h(विक 13) lor htu k(rain 13) 2. the slope of the tangent when ys 513 -8, ho ħ 9th +3 √4th 13 2-1, hvo th₂o
Transcribed Image Text:Ex. 2 Find the slope of the tangent to y=-x²+2x+6 for the point when x=5 @x= 5+h y=(3+h)² + 2(5+h) +6 -25-10h-h² +10-2h+6 =-9-8h-h² (5th, -9-8h-1²) =lim X (-8-h), h+0 100 -8-h Find 'y' coordinate @ y = -(3) ² + 2(5) + 6 = -25+10+6 --9 : the point is (5,-9) meon= Rim f(sth)-f(s) 5th-3 h+o = fim - 9-8h-h² - (-a) ho 3th-3 -8h-h² - Rim Ex 3. Determine the slope of the tangent to f(x)- OP (3,4) X = 3+h f(31h)= 3+ha9 31h = 12+h 3+h .: the slope of the tangent at paint Pis -1, hvo x=51h f(son) (Sthis = √9th : the slope of the tangent at 4-5 is thro Mion" 2+9 at P(3,4) X nº fim +(3+h)-f(3) 3+h-3 12th -U =-8, hvo = Rum ho Ex 4. Find the slope of the tangent to f(x)=√x+4 atx=5 fls) = (344 = lim 2+0 lim hao = lim em hinh ma h (12th ~ - 4 (3+h) ) = =h 3th + 12th-12-4h. 3+h h - emm 9-1-9 nno mtan= lim f(s+h)-f(3) 5th-5 Tain -3. -3 31h h(विक 13) lor htu k(rain 13) 2. the slope of the tangent when ys 513 -8, ho ħ 9th +3 √4th 13 2-1, hvo th₂o
A TANGENT is the straight line that BEST approximates a curve locally at a given point. The slope at that point is defined as the slope of the tangent to the curve at that point. Two problems in Calculus: 1) Slope of the tangent to the curve 2) Area under the curve Ay Recall: AX More importantly, the slope is the rate of change of y with regards to x. m= y₂-y₁ Ex 1: Determine the slope of the tangent to y=x² at P(2,4). Meront Pa tangent at P m Pla fall (2th, f(zh)) ; the slope of the tangent at Point Pis 4th, hvo f(2+h)-(2) 2th 2 = (2+h) ³-4 21h-2 = 4+4h+h²-4 h = 4h+h² h = w[4+h) Tangent line The slope of the tangent to a curve at a point, P, is the limiting slope of the secant PQ as the point Q slides along the curve to point P. le: the slope of the tangent is the limit of the slope of the secant as Q approaches Palong the curve. Ql+ha+h) P mpg = 4th Mton - Rim (41h) =4 = 4+h, hvo Slope of a Tangent as a Limit The slope of the tangent to the graph y=f(x) at point P(a.f(a)) is Fle+A)-(e), if this limit exists. = A lim² A means os 'n' gets closer to 0, 4th approaches 4,
Transcribed Image Text:A TANGENT is the straight line that BEST approximates a curve locally at a given point. The slope at that point is defined as the slope of the tangent to the curve at that point. Two problems in Calculus: 1) Slope of the tangent to the curve 2) Area under the curve Ay Recall: AX More importantly, the slope is the rate of change of y with regards to x. m= y₂-y₁ Ex 1: Determine the slope of the tangent to y=x² at P(2,4). Meront Pa tangent at P m Pla fall (2th, f(zh)) ; the slope of the tangent at Point Pis 4th, hvo f(2+h)-(2) 2th 2 = (2+h) ³-4 21h-2 = 4+4h+h²-4 h = 4h+h² h = w[4+h) Tangent line The slope of the tangent to a curve at a point, P, is the limiting slope of the secant PQ as the point Q slides along the curve to point P. le: the slope of the tangent is the limit of the slope of the secant as Q approaches Palong the curve. Ql+ha+h) P mpg = 4th Mton - Rim (41h) =4 = 4+h, hvo Slope of a Tangent as a Limit The slope of the tangent to the graph y=f(x) at point P(a.f(a)) is Fle+A)-(e), if this limit exists. = A lim² A means os 'n' gets closer to 0, 4th approaches 4,
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS