1. a. Use slopes to show that A (3,1), B (9,4), C (4,10) and D (-2,7) are the vertices of a parallelogram. b. Find an equation of the line passes through the point (2,8) and parallel to the line passing through (-3,5) and (3,2).

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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МАТ-116
Assignment – I
1. a. Use slopes to show that A (3,1), B (9,4), C (4,10) and D (-2,7) are the vertices of a
parallelogram.
b. Find an equation of the line passes through the point (2,8) and parallel to the line passing
through (-3,5) and (3,2).
2. a. Find the center and radius of the circle x² + 2x + y² – 4y + 4 = 0 and sketch its graph.
b. Find the standard form of the equation of the circle with endpoints of a diameter at (8,3)
and (0,1).
3x? + 3x +1 if x < -3
if - 3<x<1
if x>1
Evaluate f(-10), f(0), f (-),f(30). What is the domain of f(x)?
3. a. Given, f(x) =
4x + 1
10
b. Find the domain of
i. f(x) = Vx? – 2x – 8 ii.
4. If an object is dropped from the top of a mountain, then the distance it has fallen after t
seconds is given by the function d(t) = 2t² + 10. Find it's average speed over the
following intervals
i.
Between Is and 6s ii. Between t = a and t = a + h.
5. a. Find the local maximum or minimum value of the following function. Find the
interval where the function is increasing and where it is decreasing?
b. Determine algebraically whether the function h(x)
is even, odd or neither.
3x2-9
Transcribed Image Text:МАТ-116 Assignment – I 1. a. Use slopes to show that A (3,1), B (9,4), C (4,10) and D (-2,7) are the vertices of a parallelogram. b. Find an equation of the line passes through the point (2,8) and parallel to the line passing through (-3,5) and (3,2). 2. a. Find the center and radius of the circle x² + 2x + y² – 4y + 4 = 0 and sketch its graph. b. Find the standard form of the equation of the circle with endpoints of a diameter at (8,3) and (0,1). 3x? + 3x +1 if x < -3 if - 3<x<1 if x>1 Evaluate f(-10), f(0), f (-),f(30). What is the domain of f(x)? 3. a. Given, f(x) = 4x + 1 10 b. Find the domain of i. f(x) = Vx? – 2x – 8 ii. 4. If an object is dropped from the top of a mountain, then the distance it has fallen after t seconds is given by the function d(t) = 2t² + 10. Find it's average speed over the following intervals i. Between Is and 6s ii. Between t = a and t = a + h. 5. a. Find the local maximum or minimum value of the following function. Find the interval where the function is increasing and where it is decreasing? b. Determine algebraically whether the function h(x) is even, odd or neither. 3x2-9
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