12 X 12
Explanation ∫ du 1 u2 = tan−1u C → Where u is a function of x Proof ∫ du 1 u2 Integration by Trigonometric Substitution u = tanθ → du = sec2θd(θ) ∫ du 1 u2 = ∫ sec2θd(θ) 1 tan2θ sec2θ = 1 tan2θ ∫ sec2θd(θ) 1 tan2θ = ∫ (1 tan2θ)d(θ) 1 tan2θ.
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Two numbers r and s sum up to \frac{1}{2} exactly when the average of the two numbers is \frac{1}{2}*\frac{1}{2} = \frac{1}{4} You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2BxC. Calculus Simplify (x^2)/ (x^ (1/2)) x2 x1 2 x 2 x 1 2 Move x1 2 x 1 2 to the numerator using the negative exponent rule 1 bn = b−n 1 b n = b n x2x−1 2 x 2 x 1 2 Multiply x2 x 2 by x−1 2 x 1 2 by adding the exponents Tap for more steps Use the power rule a m a n = a m n a m a n = a m n to combine exponents. Can be used to divide mixed numbers 1 2/3 4 3/8 or can be used for write complex fractions ie 1/2 1/3 An asterisk * or × is the symbol for multiplication Plus is addition, minus sign is subtraction and () is mathematical parentheses.
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Simplify (x^ (1/2))^2 (x1 2)2 ( x 1 2) 2 Multiply the exponents in (x1 2)2 ( x 1 2) 2 Tap for more steps Apply the power rule and multiply exponents, ( a m) n = a m n ( a m) n = a m n x 1 2 ⋅ 2 x 1 2 ⋅ 2 Cancel the common factor of 2 2 Tap for more steps Cancel the common factor. Explanation Now we have the form above with u = x 2, so we evaluate the limit Jim, awesome What this limit really represents is essentially the horizontal asymptote y = e2, reflecting the function's long term graphical behavior. 4x2=1 Two solutions were found x = 1/2 = 0500 x = 1/2 = 0500 Rearrange Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation.
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