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MatroZZZ [7]
3 years ago
13

Solve the following equation: lim x->0 sin3x/5x^3-4x.

Mathematics
1 answer:
goblinko [34]3 years ago
3 0
Usual limit of sin is sinX/X--->1, when X--->0

sin3x/5x^3-4x=0/0?, sin3x/3x--->1 when x --->0, so sin3x/5x^3-4x=                    [3x. sin3x / 3x] /(5x^3-4x)=(sin3x / 3x) . (3x/5x^3-4x)
   =(sin3x / 3x) . (3/5x^2- 4)
finally lim  sin3x/5x^3-4x=lim (sin3x / 3x) .(3/5x^2- 4)=1x(3/-4)= - 3/4
                 x----->0            x---->0
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For an A.P. ,The first two term are -3, 4. The 21st term is
Dahasolnce [82]

Answer:

The 21st term is 137.

Step-by-step explanation:

Arithmetic progression:

In an arithmetic progression the difference between consecutive terms is always the same, and its called common difference.

The nth term is given by:

a_n = a_1 + (n-1)d

In which a_1 is the first term and d is the common difference.

The first two terms are -3, 4.

This means that a_1 = -3, d = 4 - (-3) = 7

So

a_n = a_1 + (n-1)d

a_n = -3 + 7(n-1)

The 21st term is

a_{21} = -3 + 7(21-1) = -3 + 140 = 137

The 21st term is 137.

4 0
3 years ago
Change the following decimals to fractions: 45
ELEN [110]

Answer:

45÷100

=0.045 is your answer

3 0
2 years ago
Which of the following expressions represents the distance between -3.9, and -4.7?
Solnce55 [7]

Answer:

d =  \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2}  }

Step-by-step explanation:

d =  \sqrt{( - 4 + 3) {}^{2} + (7 - 9) {}^{2}  }

d =   \sqrt{(1 + 4)}  =  \sqrt{5}

7 0
3 years ago
Click and drag like terms onto each other to simplify fully. 1+x^2-3+2y+7x^2+3+3y
Mandarinka [93]

Answer:

8x^2 + 5y + 1

Step-by-step explanation:

1 + x^2 - 3 + 2y + 7x^2 + 3 + 3y

group like terms

= x^2 + 7x^2 + 2y + 3y + 1 - 3 + 3

add similar items

= 8x^2 + 2y + 3y + 1 - 3 + 3

add similar items

= 8x^2 + 5y + 1 - 3 + 3

= 8x^2 + 5y + 1

5 0
2 years ago
Solve (3/x-3) =(x/x-3)-(3/2) for x and determine if the solution is extraneous or not
Darya [45]
3/(x-3)=x/(x-3)-3/2
6/2(x-3)=2x/2(x-3)-3(x-3)/2(x-3)
6=2x-3(x-3)
6=2x-3x+9
x=3

x=3 makes the denominator x-3 a zero, so the solution is extraneous, 
3 0
3 years ago
Read 2 more answers
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