A real number which is not a rational is an irrational number. π=3.14 ... in an irrational numbers.

The function is a rational function. Because the limits of the numerator and the denominator are equal to 0, we need to factorise the ratio which follows as

[(x² -2x - 35) / (x - 7)] = [(x - 7) (x + 5)] / x-7 = x + 5. 

Following the limit rules, we find lim_x›7 x + 5 = 7 + 5 = 12.

We need to equate the demand of elasticity to one,

The answer is D.

z = u⁴ v² – u² – v² ; ?z / ?u = 4 u³ v² – 2 u ; at u = v = -1, ?z / ?u = -2 . pg. 188. Correct answer is A.

0 ; Since the degree of the numerator is less than the degree of the denominator. pg. 114. Correct answer is D.

y=kx,

(5x²+k²x²) / (x²+k²x²)=x²(5+k²) / x²(1+k²)=(5+k²) / (1+k²).

By the way we have an answer depending on k, the limit does not exist.

Local minimum : C'(x) = 4 x – 120 = 0 ; x = 30 ; C'' (30) = 4 > 0 . pg. 164. Correct answer is A.

The total revenue function for the product is,

R(x)=p*x=10-(2x/4)*x=10x-2(x^2)/4

Since the total profit is the difference between the total revenue and the total cost function we have

The answer is C.

The answer is A.

P(x) = R(x) – C(x) ; R(x) = (40 – (x / 2)) x ; C(x) = 48 + 4 x ; P(x) = -0.5 x² + 36 x – 48 ; P'(x) = -x + 36 = 0 ; x = 36 ; P(36) = 600 . pg. 164. Correct answer is C.

0.2 ; limit of a constant is itself. pg. 107. Correct answer is C .

The answer is A.

(2 – 05) (4 – 1) = 4.5. pg. 110. Correct answer is A.

?f / ?y = x e^xy + 2xy – x ; ?²f / ?y² = x² e^xy + 2x . pg. 183. Correct answer is E.

$f(x,y)=\ln (2x+y) \; z0=ln1=0$

$?f/?x\; =2/(2x+y)\; =2$

$?f/?y=1/(2x+y)=1$

$then,\; z-0=2(x-(-1))+1(y-3)$

$z=2(x+1)+y-3$

$z=2x+y-1$

We can decrease the number of unknown variables to one by substitution.

Since 120=2x+4y, y=(120-2x)/4=30-0.5x

Then we can rewrite his utility function as U(x,y)=x^0.5y^0.5=U(x)=x^0.5(30-0.5x)^0.5=(x(30-0.5x))^0.5=(30x-0.5x²)^0.5

For the maximum utility the first derivative of utility with respect to x must be equal to zero. Thus:

Ux=0.5(30-x)(30x-0.5x²)^-0.5=0

30-x=0, which means x=30. Substituting this in y=30-0.5x=15. Thus the utility maximizing combination of (x,y)=(30,15)

If f(x)=h(x)/g(x) then f '(x)=(h '(x)g(x)-g '(x)h(x))/g²(x) from the Quitent rule.

So if f(x)=(3x²+5x)/(2x-1),

then:

f '(x)=(h '(x)g(x)-g '(x)h(x))/g²(x)=((6x+5)*(2x-1)-2(3x²+5x))/(2x-1)²

=(12x²+4x-5-6x²-10x)/(2x-1)²

=(6x²-6x-5)/(4x²-4x+1)

The function is a rational function. Since the degree o the numerator is greater than the degreeof the denominator, the following result is true:

. The answer is A.

x²y-3y²+2zx=0

2xydx+x²dy-6ydy+2xdz+2zdx=0

Since we are interested in dz/dx we can take dy=0 (y doesnt is constant).

So 2xydx+2xdz+2zdx=0 then 2xdz=-2xydx-2zdx and divind both sides to dx we obtain 2xdz/dx=-2xy-2z

so dz/dx=(-2xy-2z)/2x=-y-2z/x