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Find the area enclosed by curve (graph) `y = x^(2)+x+1` amd its tangent at `(1,3)` between ordiantes `x = - 2` and `x = 1`.

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To find the area enclosed by the curve \(y = x^2 + x + 1\) and its tangent at the point \((1, 3)\) between the ordinates \(x = -2\) and \(x = 1\), we will follow these steps: ### Step 1: Find the equation of the tangent line at the point (1, 3) 1. Differentiate the curve \(y = x^2 + x + 1\) to find the slope of the tangent. \[ \frac{dy}{dx} = 2x + 1 \] ...
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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -High Level Problem
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  5. Find the value of a(0 lt a lt 1) for which the following definite inte...

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  14. Let f(x) be a continuous function AA xepsilonR, except at x=0, such th...

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  15. Given that lim(nrarroo) sum(r=1)^(n) (log(e)(n^(2)+r^(2))-2log(e)n)/n ...

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  16. Given that lim(x to 0)(int(0)^(x)(t^(2))/(sqrt(a+t))dt)/(bx-sinx) = 1,...

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  17. Sketch the graph of cos^(-1)(4x^3-3x) and find the area enclosed betwe...

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  18. Consider a square with vertices at (1, 1), (-1, 1), (-1, -1) and (1, -...

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  20. Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x l...

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  21. Find the area of region : {(x,y) : 0 le y le x^(2) + 1, 0 le y le x + ...

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