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Q. 12

Expert-verifiedFound in: Page 988

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

Fill in the blanks to complete the limit rules. You may assume that $\underset{\mathbf{x}\to \mathbf{a}}{lim}\u200af\left(\mathbf{x}\right)$ and$\underset{\mathbf{x}\to \mathbf{a}}{lim}\u200ag\left(\mathbf{x}\right)$ exists and that k is a scalar.

$\underset{\mathbf{x}\to \mathbf{a}}{lim}\u200akf\left(\mathbf{x}\right)=$

Ans: $\underset{\mathbf{x}\to \mathbf{a}}{lim}\u200akf\left(\mathbf{x}\right)=k\underset{\mathbf{x}\to \mathbf{a}}{lim}\u200af\left(\mathbf{x}\mathbf{\right)}$ (According to rules of limit.)

given, $\underset{\mathbf{x}\to \mathbf{a}}{lim}\u200akf\left(\mathbf{x}\right)=$

The limit of constant times a function is equal to the constant times the limit of the function.

like if C is a scalar then, $\underset{\mathbf{x}\to \mathbf{a}}{lim}\u200aCf\left(\mathbf{x}\right)=C\underset{\mathbf{x}\to \mathbf{a}}{lim}\u200af\left(\mathbf{x}\mathbf{\right)}$

That's why

$\underset{\mathbf{x}\to \mathbf{a}}{lim}\u200akf\left(\mathbf{x}\right)=k\underset{\mathbf{x}\to \mathbf{a}}{lim}\u200af\left(\mathbf{x}\mathbf{\right)}$

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