Determine dy & dy if y = cos ( x2 + 1) - x, Mathematics

Assignment Help:

Determine dy & Δy  if y = cos ( x2 + 1) - x as x changes from x = 2 to x = 2.03 .

 Solution

Firstly let's deetrmine actual the change in y, Δy .

Δy = cos (( 2.03)2  + 1) - 2.03 - (cos (22  + 1) - 2) = 0.083581127

Now let's obtain the formula for dy.

dy = (-2 x sin ( x2 + 1) -1) dx

Next, the change in x from x = 2 to x = 2.03 is Δx = 0.03 and therefore we then suppose that dx ≈ Δx = 0.03 .  It gives an approximate change in y of,

            dy = (-2 ( 2) sin (22  + 1) -1)(0.03) = 0.085070913

We can illustrates that actually we do have that Δy ≈ dy provided we keep ?x small.

 

 


Related Discussions:- Determine dy & dy if y = cos ( x2 + 1) - x

Space geometry, a sketch of two dimensional system

a sketch of two dimensional system

Factor, 27-125 a power -135a +225a power2

27-125 a power -135a +225a power2

Project, elliptical path of celestial bodies

elliptical path of celestial bodies

If a differential equation does have a solution can we find?, It may seem l...

It may seem like an odd question to ask and until now the answer is not all the time yes. Just as we identify that a solution to a differential equations exists does not implies th

Reduced Row-Echelon Form, The augmented matrix from a system of linear equa...

The augmented matrix from a system of linear equations has the following  reduced row-echelon form (a)  How many equations are there in the system?  (b)  How many variab

Generic rectangle puzzle solve, What do you need to multiply 30 by to get 1...

What do you need to multiply 30 by to get 1500? This will give you the top edge length of the rectangle. Can you then figure out what must go below the 30 in order to get the area

What was the total cost of her order, Leslie ordered a slice of pizza for $...

Leslie ordered a slice of pizza for $1.95, a salad for $2.25, and a soda for $1.05. What was the total cost of her order? The cost of every item must be added together; $1.95 +

What is the average number of miles lori ran, Lori ran (5)1/2 miles Monday,...

Lori ran (5)1/2 miles Monday, (6)1/4 miles Tuesday (4)1/2 miles Wednesday and (2)3/4 mile on Thursday what is the average number of miles lori ran ? To find the average, add

Derivatives to physical systems, Derivatives to Physical Systems: A st...

Derivatives to Physical Systems: A stone is dropped into a quiet lake, & waves move within circles outward from the location of the splash at a constant velocity of 0.5 feet p

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd