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

Evaluate `lim_(x to (pi)/(4)) (1 - tanx)/(x - (pi)/(4))`

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To evaluate the limit \( \lim_{x \to \frac{\pi}{4}} \frac{1 - \tan x}{x - \frac{\pi}{4}} \), we can follow these steps: ### Step 1: Direct Substitution First, we substitute \( x = \frac{\pi}{4} \) into the expression: \[ 1 - \tan\left(\frac{\pi}{4}\right) = 1 - 1 = 0 \] and ...
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AAKASH INSTITUTE ENGLISH-LIMITS AND DERIVATIVES -Example
  1. Evaluate lim(x to 0) ("sin"^(2) (3x//2x))/(x)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. (i) lim(x to 0) (a^(x) - 1)/(log(a)(1 + x)), a gt 0 (ii) lim(x t...

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  19. Find (dy)/(dx) when (i) Y = (x)/(log(a)X) (ii) Y = cos x cos 2x co...

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  20. Evaluate the following limits (i) lim(x to (pi)/(2)) tan^(2) x [sqr...

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