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Find the derivative of cos(2x+1) w.r.t. ...

Find the derivative of `cos(2x+1)` w.r.t. x from first principle.

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To find the derivative of the function \( f(x) = \cos(2x + 1) \) with respect to \( x \) using the first principle of derivatives, we will follow these steps: ### Step 1: Write the definition of the derivative using the first principle. The derivative of a function \( f(x) \) from first principles is given by: \[ \frac{dy}{dx} = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} \] ...
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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Verify Rolle's theorem for the function f(x)=\ x^2-5x+6 on [2, 3].

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  2. Using matrices, solve the following system of equations: 2x-y+z= -3, ...

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  3. Find the derivative of cos(2x+1) w.r.t. x from first principle.

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  4. Evaluate: \lim{x\rightarrow0}\ ((sqrt(1+x)\ -\ sqrt(1-x))/(sin^(-1)x))

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  5. Solve the following differential equation : ("x"^2-1)"dy"/("dx")+2"xy...

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  6. Using integration calculate the area of the region bounded by the t...

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  7. Evaluate int0^2(2x^2+\ x+5)dx as limit of a sum.

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  8. Solve the following differential equation: ("y"^2- "x"^2)"dy"=3"x y ...

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  9. Verify that "y"="Acos x"-"Bsinx" is solution of the differential eq...

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  10. A window is in the form of a rectangle surmounted by a semi-circle. ...

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  11. An open box, with a square base, is to be made out of a given quanti...

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  12. Find the intervals in which the function "f"("x")="x"^"3"- "12"x^2+ ...

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  13. Evaluate: int sqrt(tan theta) d theta

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  14. Using matrices, solve the following system of equations: 3"x"-"y"+"...

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  15. Differentiate sqrt ("tan x")" w.r.t x from first principle.

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  16. Evaluate: \lim{x\rightarrow \infty }sqrt(x^2+x+1)-x

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  17. Prove that int"o"^"a""f"("x")"dx"=""int"o"^"a""f "("a"-"x")"dx"dot

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  18. Evaluate : int("x"^2+1)/(("x"+1)^2)"dx"

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  19. Evaluate: int1/(1+x+x^2+x^3)\ dx

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  20. Find the coordinates of the point where the line ("x"+1"")/2=("y"+2...

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