Calculus Answers

Q. Draw the graph of following functions on graph paper.
(i)y=x2
(ii)y=x2+1
(iii)y2=x
(iv)y2=4x+2
(v)y2=x-1
(vi)x2=4y
(vii)x2=4y-1
(viii)x2+y2=1
(ix)x2-y2=1
(xx)x2+y2=0

: Which of the following could be an example of a function with a range (-∞, -a] and a domain [ -b, ∞) where a > 0 and b > 0?

A: f(x) = 3√(x-b) + a
B: f(x) = - 3√x + a – b
C: f(x) = - √x + b - a
D: f(x) = √x – a + b


: Which of the following are true statements?
Check all that apply.

The graph of f(x) = -1/2 √x will look like the graph of f(x) = √x but will reflect it about the x-axis and shrink it vertically by a factor of ½

The graph of f(x) = -1/2√x will look like the graph of f(x) = √x but will shrink it vertically by a factor of ½

The graph of f(x) = -1/2√x will look like the graph of f(x) = √x but will shrink it horizontally by a factor of ½

f(x) = -1/2√x has the same domain but a different range as f(x) = √x

The circle given by x^2 + y^2 – 4x – 10 = 0 can be written in standard form like this: (x – h)^2 + y^2 = 14

What is the value of h in this equation. _________


What is the radius for the circle given by the equation x^2 + (y -1)^2 = 12
Round your answer to the nearest thousandth. ______



A degenerate circle is:
1: a circle with radius r = 0
2: a point.
3: a line.

A: All three are correct
B: only 2 is correct
C: only 3 is correct
D: 1 and 2 are correct
E: only 1 is correct

Which functions in the table below give values that could not come from exponential functions?

x -3 -2 -2 0 1 2 3
f(x) 0.67 1.11 1.82 3 4.95 8.15 13.45
g(x) 0.125 0.25 0.5 1 2 4 8
h(x) 0.25 0.5 0.75 1 1.25 1.5 1.75
k(x) 64 16 4 0 0.25 0.0625 0.0156

If $1,000 is invested in an account that pays 3% interest compounded annually, an expression that represents the amount in the account at the end of two years can be given by which of the following equations?

A: 1000(1.03)^2
B: 1000(0.3)^2
C: 1000 + 0.2^3

Which of the following could be an example of a function with a domain (-∞, ∞) and a range (-∞ , 4)
Check all that apply

y = - (3)^x - 4

y = - (0.25)^x - 4

y = - (0.025)^x + 4

y = - (3)^x + 4

(a^3 b^12 c^2) x (a^5 c^2)
---------------------------------- =
(b^5 c^4)^0

A: a^15 b^12 c^4
B: a^8 b^12 c^4
C: a^14 b^15 c^9
D: a^8 b^17 c^8


81^3/4
------------ =
81^1/2


A: 9
B: (81/3)^-1/2
C: 27
D: 3

The function f(x) = -a^x + 4 will never cross the x-axis.

True
False

Q. If f(x,y)=tan^(-1)⁡〖(2xy/〗X2+y2)
Then prove ∂2f/∂x2+∂2f/∂y2=0

Q.If f(x,y) =ln⁡〖((x^2+y^2)/xy)〗
Then prove that
∂2f/∂x2+∂2f/∂y2=0

Q. If f(x,y)=((x^2+y^2)/xy)
Then prove that ∂2f/∂x2+∂2f/∂y2=0

please help me this question
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