Use left end points What does this sum represent 3 Express the limit as a

# Use left end points what does this sum represent 3

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vals. Use left end-points. What does this sum represent? 3. Express the limit as a definite integral on the given interval. (a) On [0,1]: lim n →∞ n X k =1 e x k 1 + x i Δ x (b) On [2,5]: lim n →∞ n X k =1 x i q 1 + x 3 i Δ x 4. Find the derivatives of the following functions: (a) g ( x ) = R x a 1 + t 2 dt (b) f ( x ) = R x 4 e x cos 2 ( θ ) 5. Evaluate the following integrals. (a) Z 1 - 1 x 100 dx (b) Z 4 1 2 + x 2 x dx (c) Z 5 - 5 e dx (d) Z π π/ 6 sin( x ) dx (e) Z 4 x 3 - 3 x 2 + 2 xdx 3

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(f) Z x p 1 - x 2 dx (g) Z sin( x ) sin(cos( x )) dx (h) Z x x - 1 dx (i) Z x cos(5 x ) dx (j) Z x 4 ln( x ) dx (k) Z ( x - 1) sin( πx ) dx (l) Z 5 x + 1 2 x 2 + x - 1 dx (m) Z x 2 x 2 + 7 x - 4 dx 6. For the following integrals, make a u -substitution, then integrate by parts. (a) Z e x dx (b) Z cos(ln( x )) dx 7. True or false: if f is not continuous, R f ( x ) dx does not exist. 4
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