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Evaluate lim(x to 0) ("sin" 4x)/(6x)...

Evaluate `lim_(x to 0) ("sin" 4x)/(6x)`

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To evaluate the limit \( \lim_{x \to 0} \frac{\sin 4x}{6x} \), we can follow these steps: ### Step 1: Identify the limit form We know that as \( x \) approaches 0, both the numerator \( \sin 4x \) and the denominator \( 6x \) approach 0. This gives us a \( \frac{0}{0} \) indeterminate form, which allows us to use L'Hôpital's Rule or manipulate the expression. **Hint:** Recognize the indeterminate form \( \frac{0}{0} \) to decide on the next steps. ### Step 2: Use the known limit property ...
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AAKASH INSTITUTE ENGLISH-LIMITS AND DERIVATIVES -Example
  1. If lim(x to 1) (x^(3) - 1)/(x - 1) = lim(x to k) (x^(4) - k^(4))/(x^...

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  2. Evaluate lim(x to 0) (sqrt(x + 2) - sqrt(2))/(x)

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  3. Evaluate lim(x to 0) ("sin" 4x)/(6x)

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  4. Evaluate lim(x to 0) ("sin"^(2) (3x//2x))/(x)

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  5. Evaluate lim(x to0 ) ("sin" 3x)/("sin" 6x)

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  6. Evaluate the following limits : Lim(x to 0) (1- cos x)/(x^(2))

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  7. Evaluate lim(x to 0) (tan x + 4 tan 2x - 3tan 3x)/(x^(2) tan x)

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  8. Evaluate lim(x to (pi)/(4)) (1 - tanx)/(x - (pi)/(4))

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  9. Let f be a real-valued function defined by f(x) = 3x^(2) + 2x + 5 Find...

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  10. Find the derivative of the following functions from the first principl...

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  11. Find the derivative of the following functions from the first principl...

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  12. Find the derivative of the following functions from first principle (i...

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  13. Find the derivative of the following functions using first principle o...

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  14. Find the derivative of the following functions using first principle o...

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  15. Find the derivative of the following functions (i) x^(3) + cos x + ...

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  16. Find the derivative of the following functions. (i) (x^(2) tan x) ...

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  17. Find the derivative of the following functions. (i) ((x + 1)/(x + 2)...

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  18. Evaluate lim(x to oo) (ax^(p) + bx^(p- 3) + c)/(a(1)x^(q) + b(1)x^(q-...

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  19. Evaluate lim(x->oo)sqrt(x)(sqrt(x-2007)-sqrt(x))

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  20. (i) underset(x to oo)(Lt) e^(x) "sin" (Ke^(-x)) (ii) lim(x to oo) ((...

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