Examen De Calculo

Nomenclatura:
Correcta Verde

• Which is the right period, amplitude and phase shift of this trigonometric function?
[pic]
• [pic]
• [pic]
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• None iscorrect.

• Indicate which is the discontinuity type of the function given.
[pic]
• Removable discountinuity
• Jump discontinuity
• Infinite discontinuity• The function is continuous.

1. [pic]
y = sin x
If we shift the function -2 units vertically and 3 units to the right, the translated function would be:
• y -2 = sinx - 3
• y - 3 = sinx + 2
• y= sin (x - 3) - 2
• y - 2  = sin (x - 3)
• None of the above.

2. [pic]
Necessary, but not sufficient condition fora function f(x) to be continuous at xo is:
 
• The function has to be defined at xo : f(xo) = yo
• The derivative must exist at x0.
• [pic]
• [pic]• None of the above.

3. [pic]
Indicate which graphic represents the following function:
y= x2 ( x + 1 )
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• [pic]
• [pic]
•[pic]
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4. [pic]
Find the derivative of the function:
[pic]
• [pic]
• [pic]
• [pic]
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• None is correct.5. [pic]
Find the derivative of the function:
log2( cos(2x) + x3)
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• [pic]
• [pic]
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• None of the above.

6. [pic]Find the equation of the line tangent to the function : f(x)=1/2 sin(x+pi/2)   at the point    x0=3pi/2.
• y = 1/2 sin (2pi)
• y = 1/2 (x - pi/2)
• y = x/2 - 3pi/4• y= x + 3pi/2
 
• None of the above.

7. [pic]
Find the maximum and minimum of this function :
f(x)= x ( x2 - 1)
in the following interval:...