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Calc 1 2.6

 

<== Calculus 1
Number Question Answer
See the work

1.

 

If (x^2)/81+(y^2)/16=1 and y(2)=(4/9)sqrt(77)      
find y'(2) by implicit differentiation.

 

-32/(36*sqrt(77))        

 

The work

Point Cost: 3

 

2.

 

If 3x^2+4x+xy=5 and y(5)=-18,      
find y'(5) by implicit differentiation.

 

-3.2

 

The work

Point Cost: 3

 

3.

 

 

 

For the equation given below, evaluate y' at
the point (2,1).

4(x^(3))y-3x^(2)=-20

y' at (2,1)=______

 

y' at (2,1)= -1.125
The work

Point Cost: 3

4.

 

For the equation given below, evaluate y' at
the point (1,2).

(2x-y)^(4)+2y^3=16

y' at (1,2)=______

 

y'= 0
The work

Point Cost: 3

5.

 

Find y' by implicit differentiation. Match
the expressions defining y implicitly with the
letters labeling the expressions for y'.


 

1. A

2. B

3. C

4. D

The work

Point Cost: 1

6.

 

 

Find dy/dx by implicit differentation:

tan(x/y)=5x+3y

 

dy/dx= y(sec(x/y)^2-5y)/(xsec(x/y)^2+3y^2)    

 

The work

Point Cost: 3

 

7.

 

 

Find dy/dx by implicit differentation:

 

dy/dx=

 

The work

Point Cost: 3

 

8.

 

 

 

 

Use implicit differentiation to find the slope of the 
tangent line to the curve

4xy^3+5xy=36

at point (4,1)

m=_______

 

m= -0.132352941176471
The work

Point Cost: 3

9.

 

 

 

Find the slope of the tangent line to the curve

sqrt(1+x^(2)y^(2))-3xy=-84

at the point (7,6)
slope=____________

 

Slope= -6/7
The work

Point Cost: 3

10.

 

 

 

Find the slope of the tangent line to the curve

4sin(x)+3cos(y)-4sin(x)cos(y)+x=3π

at the point (3π, 7π/2)

 

slope= 1
The work

Point Cost: 3

11.

 

 

 

Find the slope of the tangent line to the curve

sqrt(3x+2y)+sqrt(3xy)=10.7

at the point (6,2)

 

slope= -(0.81980107453/1.71320071636)
The work

Point Cost: 3

12.

 

 

 

 

Find the slope of the tangent line to the curve

(x^(2)/36)-(y^(2)/1)=1

at the point (-9,1/6(sqrt(45)))

m=______
b=_______

 

m= -0.223606797749979
b= -0.894427190999916
The work

Point Cost: 3

13.

 

 

 

Find the equation of the tangent line to the curve
2(x^2+y^2)^2= 25(x^2-y^2) at the point (3,-1).
The equation of this tangent line can be written in
the form y = mx+b
where m is:_________
and where b is:______

 

m= 0.692307692307692
b= -3.07692307692308

 

The work

Point Cost: 3

14.

 

 

Let x^3+y^3=65. Find y''(x) at the point (4,1).

y''(4)=_____

 

y''(4)= -520

 

The work

Point Cost: 3