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3 years ago

Can someone Help ASAP

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

4 0

Answer:

option no.B - 3+ x <7

Step-by-step explanation:

hope it helps you

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(a) Find all points where the function f(z) = (x^2+y^2-2y)+i(2x-2xy) is differentiable, and compute the derivative at those poin

Olenka [21]

Answer:

The given function is differentiable at y = 1.

At y = 1, f'(z) = 0

Step-by-step explanation:

As per the given question,

$f(z)\ = (x^{2}+y^{2}-2y)+i(2x - 2xy)$

Let z = x + i y

Suppose,

$u(x,y) = x^{2}+y^{2}-2y$

$v(x,y) = 2x - 2xy$

On computing the partial derivatives of u and v as:

$u'_{x} =2x$

$u'_{y}=2y -2$

And

$v'_{x} =2-2y$

$v'_{y}=-2x$

According to the Cauchy-Riemann equations

$u'_{x} =v'_{y} \ \ \ \ \ \ \ and\ \ \ \ \ \ u'_{y} = -v'_{x}$

Now,

$(u'_{x} =2x) \neq (v'_{y}=-2x)$

$(u'_{y}=2y -2) \ = \ (- v'_{x} =-(2-2y) =2y-2)$

Therefore,

$u'_{y}=- v'_{x}$ holds only.

This means,

2y - 2 = 0

⇒ y = 1

Therefore f(z) has a chance of being differentiable only at y =1.

Now we can compute the derivative

$f'(z)=\frac{1}{2}[(u'_{x}+iv'_{x})-i(u'_{y}+iv'_{y})]$

$f'(z) =\frac{1}{2}[(2x+i(2-2y))-i(2y-2+i(-2x))]$

$f'(z) = i(2-2y)$

At y = 1

f'(z) = 0

Hence, the required derivative at y = 1 , f'(z) = 0

7 0

3 years ago

Factor y2 + 5y + 6.

Phoenix [80]

This is a notable trinomial.

You have to find two number which summed give 5 and multiplied give 6

In this case 2 and 3

2+3 = 5 and 2*3 = 6

So (y+2)(y+3)

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4 years ago

A college has a student to teacher ratio of 30 to 2. If there are 186 teachers at the college, how many students attend the coll

kakasveta [241]

Answer: 2790 students

Step-by-step explanation: With the given information, you could set up a ratio of 30/2 = x/186. When you cross multiply that, you get 2790.

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3 years ago

Find the slope of the line between the following two points (-5,-1), (-1,9)

Basile [38]

Answer: The slope of the line is -2

Step-by-step explanation:

We can use the formula $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$ to solve to for this

$\frac{-9--1}{-1--5} \\\frac{-8}{4} \\-2$

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3 years ago

Drag numbers to the blanks to complete the quadratic function, f(x), that has zeros at x = -2 and x = 5.

sergij07 [2.7K]

Answer:-12 abs 3

Step-by-step explanation:

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3 years ago

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