3 years ago

What is 1^∞ equal to?

Mathematics

1 answer:

Alex Ar [27]3 years ago

7 0

The result is undefined.

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Use implicit differentiation to find an equation of the tangent line to the curve at the given point. 7x2 + xy + 7y2 = 15, (1, 1

riadik2000 [5.3K]

Assume $y=y(x)$ .

$7x^2+xy+7y^2=15$
$\dfrac{\mathrm d}{\mathrm dx}[7x^2+xy+7y^2]=\dfrac{\mathrm d}{\mathrm dx}[15]$
$14x+y+x\dfrac{\mathrm dy}{\mathrm dx}+14y\dfrac{\mathrm dy}{\mathrm dx}=0$
$\dfrac{\mathrm dy}{\mathrm dx}(x+14y)=-(14x+y)$
$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{14x+y}{x+14y}$

The slope of the tangent line to the curve at $(a,b)$ is then $-\dfrac{14a+b}{a+14b}$ , so the tangent to $(1,1)$ has slope

$\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=-\dfrac{15}{15}=-1$

The point-slope form of the tangent line is then

$y-1=-(x-1)\iff y=-x+2$

7 0

3 years ago

explain how to find the greatest number of identical arrangements that can be made with 54 roses and 42 tulips with no flowers l

asambeis [7]

Work out the Greatest Common Factor for both numbers

54 42
1×54 1×42
2×27 2×21
3×18 3×14
6×9 6×7

The common factors are: 1, 2, 3 and 6

The greatest common factor is 6

There are 6 identical arrangements that can be made

8 0

3 years ago

Read 2 more answers

2(x + 7) + x = 20 how to solve and what's the answer?

Vlad [161]

2(x + 7) + x = 20

Distribute 2 inside the parentheses.

2x + 14 + x = 20

Combine like terms.

3x + 14 = 20

Subtract 14 from both sides.

3x = 6