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Elodia [21]
3 years ago
14

Factor 13x2 + 13x + 9x + 9 = 0​

Mathematics
1 answer:
Alex787 [66]3 years ago
8 0

Answer:

\Large \boxed{x=\frac{-9}{13} \ \ \mathrm{or} \ \ x = -1}}

Step-by-step explanation:

13x^2  + 13x + 9x + 9 = 0

Factor the expression.

13x(x+1)+9(x+1)=0

Take (x + 1) as a common factor.

(13x+9)(x+1)=0

Set factors equal to 0.

First possibility:

13x + 9 = 0

13x=-9

\displaystyle x=\frac{-9}{13}

Second possibility:

x+1=0

x=-1

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Given f(x) = (lnx)^3 find the line tangent to f at x = 3
kirill [66]
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We must the tangent line at x = 3 of the function:

f(x)=(\ln x)^3.

The tangent line is given by:

y=m*(x-h)+k.

Where:

• m is the slope of the tangent line of f(x) at x = h,

,

• k = f(h) is the value of the function at x = h.

In this case, we have h = 3.

1) First, we compute the derivative of f(x):

f^{\prime}(x)=\frac{d}{dx}((\ln x)^3)=3*(\ln x)^2*\frac{d}{dx}(\ln x)=3*(\ln x)^2*\frac{1}{x}=\frac{3(\ln x)^2}{x}.

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3) The value of k is:

k=f(3)=(\ln3)^3

4) Replacing the values of m, h and k in the general equation of the tangent line, we get:

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Plotting the function f(x) and the tangent line we verify that our result is correct:

Answer

The equation of the tangent line to f(x) and x = 3 is:

y=(\ln3)^2*(x-3)+(\ln3)^3

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1 year ago
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