document.write( "Question 1154021: limit x->0 (e^x^2 - e^x^3)/3x^2
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Algebra.Com's Answer #776432 by ikleyn(52863) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Start from standard expansion of Calculus for \r\n" );
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document.write( "     = 1 + t +  +  + . . .               (1)\r\n" );
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document.write( "Substitute one time  t = x^2  into expansion  (1)  to get\r\n" );
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document.write( "    e^(x^2) = 1 + x^2 +  +  + . . .         (2)\r\n" );
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document.write( "Substitute next time  t = x^3  into expansion  (1)  to get\r\n" );
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document.write( "    e^(x^3) = 1 + x^3 +  +  + . . .         (3)\r\n" );
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document.write( "Subtract (3) from (2). You will get\r\n" );
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document.write( "    e^(x^2) - e^^(x^3) = x^2 - x^3 + the terms of the converging series with degrees of  \"x\"  higher than or equal to 4.\r\n" );
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document.write( "Therefore\r\n" );
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document.write( "     = 1 - x + the terms of the converging series with degrees of  \"x\"  higher than or equal to 2.     (4)\r\n" );
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document.write( "Thus, when you take the limit at x--> 0 of  ,  you will get  .     ANSWER\r\n" );
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document.write( "The rest of the terms contribute 0 (zero) to this limit.\r\n" );
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\n" ); document.write( "\n" ); document.write( "I wrote this post, because arguments of @MathLover1 are I N V A L I D.\r
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\n" ); document.write( "\n" ); document.write( "Had I answered this question as @MathLover1 did it, with expressions $\"0%2F0\"$ on the way, I would loose my reputation FOREVER\r
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