Find the limit: mathop {lim }limits_{x to -1} | vedclass

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(B) The given expression is a polynomial function $f(x) = 1+x+x^{2}+ \dots +x^{10}$.Since polynomial functions are continuous everywhere,the limit as

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$1$

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(B) The given expression is a polynomial function $f(x) = 1+x+x^{2}+ \dots +x^{10}$.Since polynomial functions are continuous everywhere,the limit as $x 	o -1$ is simply the value of the function at $x = -1$.Substituting $x = -1$ into the expression:$f(-1) = 1 + (-1) + (-1)^{2} + (-1)^{3} + (-1)^{4} + (-1)^{5} + (-1)^{6} + (-1)^{7} + (-1)^{8} + (-1)^{9} + (-1)^{10}$$f(-1) = 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1$Grouping the terms: $(1-1) + (1-1) + (1-1) + (1-1) + (1-1) + 1$$f(-1) = 0 + 0 + 0 + 0 + 0 + 1 = 1$Therefore,the limit is $1$.

Find the limit: $\mathop {\lim }\limits_{x \to -1} (1+x+x^{2}+ \dots +x^{10})$

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