golroo

A piece of wire x m long is cut into two pieces, the length of the first piece being 18 m. The first piece is bent into a circle, and the other is bent into a rectangle with length twice the width. Give an expression for the total area A enclosed in the two shapes in terms of x.

1-Find the interval(s) where the following functions is increasing and interval(s) where the functions is decreasing

a)f(x)=2x^2 +x+1,

b) f(x) = x /(x+1)2

c) f(x) = x^2e^(−x)

2-Determine where the function is concave upward and where it is concave downward:

(a) f(x) = 3x^4 −6x^2 +x−8.

(b) f(x) = e^(x2−9).

1-Find the interval(s) where the following functions is increasing and interval(s) where the functions is decreasing

a)f(x)=2x^2 +x+1,

b) f(x) = x /(x+1)2

c) f(x) = x^2e^(−x)

2-Determine where the function is concave upward and where it is concave downward:

(a) f(x) = 3x^4 −6x^2 +x−8.

(b) f(x) = e^(x2−9).

g(x) = (2x-3.5)/(2x-12.25)^2

find the concavity, inflection points, x and y intercept , relative maximum and minimum ,increasing decreasing?

please explain your work I really want to learn this.

cheers!

Test f(x)=−5x^4−6x^3+6 for concavity and inflection points.

simplify:

xln(x)−8+2ln(x)−4x=0

Simplify ln(a^2−b^2)−ln(a−b) as much as possible.

thank you!

Simplify the following please:

[(log 19 (125))/ (log 19 (25))]

An equation of the tangent line to the curve

y=f(x)=x(3cosx−9sinx)

at the point (3pi, f(3pi) is:

Note: Please follow these instructions carefully:

(a) Express f(3pi) and f(3pi) in terms of . Simplify those expressions by evaluating the exact values of sin(3pi) and cos(3pi).

(b) Your answer should be in the form ax+m. When calculating a and m, approximate pi by 3.14.

Let f(x) = 2x^3 - 9x^2 + 12x -2. Then

a) Show that f(x) = 0 has a root between x = 0 and x = 1.

b) Use the Newton-Raphson method to find the zero of f with x0 = 0. (Find the root in the precision

of 4 decimal places)

1a) Find the derivatives of the following functions:

1) f(x) = (ln x) /x

(2) f(x) = 2xe^3x + 2^x.

b) Use logarithmic differentiation to find the derivatives of the functions:

(i) y = (x + 1)^20(x + 2)^30

(ii) y = (ln x)^x.

A water trough is 8 m long and its cross-section is an isosceles triangle which is 120 cm wide at the top, and the height is 60 cm. The trough is not full. Give an expression for V, the volume of water in the trough in cm3, when the depth of the water is d cm.

Thank you!

find dy/dx by implicit differentiation

a) y^3 + 2sqrf(xy) = 3xy^2+ y

b) use a differential to approximate 3^√27.01+(1/3^√27.01)

Please explain your answer as I really need to learn this, thank you for your time.

find dy/dx by implicit differentiation

a) y^3 + 2sqrf(xy) = 3xy^2+ y

b) use a differential to approximate 3^√27.01+(1/3^√27.01)

Please explain your answer as I really need to learn this, thank you for your time.

Don Valley West, an apartment complex, has 100 two-bedrooms units. The monthly profit (in

dollars) realized from renting x apartments is

P(x)=−10x^2 +1760x−50,000

(a) What is the actual profit realized from renting the 51st unit, assuming that 50 units have already been rented?

(b) Compute the marginal profit when x = 50 and compare your results with that obtained in part (a).

I tried finding the derivative of P(x)

P'(x)= -20x+1760 then substitute 51 and 50 for x but my answer is wrong, any help is highly appreciated. thank you!

1- use product and quotient rule to fid f'(x)

f(x)= [(2x+3)(3x-4)]/(x^2+3)

simplify your answer.

2- use chain rule to find f'(x)

f(x)=(x^2+1/x)^3/2

Don Valley West, an apartment complex, has 100 two-bedrooms units. The monthly profit (in dollars) realized from renting x apartments is :

P(x)=−10x2 +1760x−50,000

(a) What is the actual profit realized from renting the 51st unit, assuming that 50 units have already been rented?

(b) Compute the marginal profit when x = 50 and compare your results with that obtained in part (a).

Thank you :)