Limits x approaches 1 of x/sin x

Check Substitution: To solve the limit of x/sin(x) as x approaches 1, we first check if we can directly substitute the value of x into the expression without causing any indeterminate forms.Calculate sin(1): Direct substitution of x = 1 gives us 1/sin(1). Since sin(1) is not equal to zero, we do not have an indeterminate form, and direct substitution is valid.Substitute Value: Calculate the value of sin(1) using a calculator or trigonometric tables. Note that 1 should be in radians, not degrees, for the calculation.Perform Division: After calculating sin(1), we find that sin(1) ≈ 0.8414709848. Now we can substitute this value into the expression to find the limit.Substitute sin(1) into the expression to get the limit: limit as x approaches 1 of x/sin(x) = 1/0.8414709848.Perform the division to find the limit: 1/0.8414709848 ≈ 1.188395105.

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Math Problems

Grade 8

Solve multi-step inequalities

Full solution

\lim_{x \to 1}\frac{x}{\text{sin}x}

Check Substitution: To solve the limit of $\frac{x}{\sin(x)}$ as $x$ approaches $1$ , we first check if we can directly substitute the value of $x$ into the expression without causing any indeterminate forms.
Calculate $\sin(1)$ : Direct substitution of $x = 1$ gives us $\frac{1}{\sin(1)}$ . Since $\sin(1)$ is not equal to zero, we do not have an indeterminate form, and direct substitution is valid.
Substitute Value: Calculate the value of $\sin(1)$ using a calculator or trigonometric tables. Note that $1$ should be in radians, not degrees, for the calculation.
Perform Division: After calculating $\sin(1)$ , we find that $\sin(1) \approx 0.8414709848$ . Now we can substitute this value into the expression to find the limit.
Perform Division: After calculating $\sin(1)$ , we find that $\sin(1) \approx 0.8414709848$ . Now we can substitute this value into the expression to find the limit.Substitute $\sin(1)$ into the expression to get the limit: limit as $x$ approaches $1$ of $\frac{x}{\sin(x)} = \frac{1}{0.8414709848}$ .
Perform Division: After calculating $\sin(1)$ , we find that $\sin(1) \approx 0.8414709848$ . Now we can substitute this value into the expression to find the limit.Substitute $\sin(1)$ into the expression to get the limit: limit as $x$ approaches $1$ of $\frac{x}{\sin(x)} = \frac{1}{0.8414709848}$ .Perform the division to find the limit: $\frac{1}{0.8414709848} \approx 1.188395105$ .