Test B review, no caluclator please help

Question

Answer 1

1)

The given curve is

3x² - 2xy + y² = 11

Apply derivative both sides with respect to x.

3(2x) - 2 ( xy' + y ) + 2y(y') = 0

6x - 2xy' - 2y  + 2yy' = 0

6x - 2y + ( 2y - 2x )y' = 0

Substitute the point ( 1 , -2 ).

6(1) - 2( -2 ) + ( 2(-2) - 2(1) )y' = 0

6 + 4 + ( - 4 - 2 )y' = 0

10 + ( - 6 )y' = 0

10 - 6y' = 0

6y' = 10

y' = 10/6

y' = 5/3

Solution : Option (d) is the Correct Choice.

Answer 2

2)

The function is 

Rewrite the numerator x² - 25 

x² - 25 = x² - 5²  = (x+5)(x-5)

Rewrite the denominator x² - 15x + 50  

 x² - 10x -5x + 50

x(x-10) -5(x-10) 

(x-10)(x-5)

 

 Option (a) is the Correct Choice.

Answer 3

3)

Rate of change in side of a cube da / dt = 2 .

Side length of cube a = 3 cm .

Surface area of cube A = 6a² .

Apply derivative with respect to t .

dA / dt = 6*2 (a) [ da / dt ] 

dA / dt = 12a [ da / dt ] 

dA / dt = 12(3) [ 2 ] 

dA / dt = 72 cm²/sec .

Option (e) is the Correct Choice.

Answer 4

(4)

Case I) The function is

For a function to be continuous, the denominator  of the function should not be zero.

x - 2 ≠ 0

x ≠ 2

  is not continuous at x = 2.

Case II) The function is

Cancel the common terms

x - 2

For a function to be continuous, the denominator  of the function should not be zero.

is continuous at x = 2.

Case III) The function is

For a function to be continuous, the denominator  of the function should not be zero.

is continuous at x = 2.

Therefore only case (I) is not continuous at x = 2 .

Option (a) is the Correct Choice .

Answer 5

(5)

The function is

Divide numerator and denominator by x²

As then

Therefore .