sample_midterm1_2B

# sample_midterm1_2B - 1 a 5 p oints E stimate u sing R...

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1' a) (5 points) Estimate, using Riemann sums, the area under the graph of {9"::i::3,"LT: tlre x;axi1 rrgm x _t ; " _ 4 byusing three approximating rectangles and right-hand endpoints. Areo. X t cl-ffi{ta1 Lt'* 3"+h.] i + +-ti + \G ") '/:( ,-/- -0un,b "'L {-\e^rtc\$rcr -surt ld b) (ro points) Find I o *by using the definition of the definite integral. Is this the area we are tryrng to approximate in part a? why or why not? Ltt', t gr)+ inr'cr&\y = ('*I.t t?* Lr=t Rw,^o-r\n brcn ; "'i\$"*b/ : L=l cx[{i, . 1 - ' 1 Vt")l Ax \-r\,/z \ / ./ ./ - r -t-f- WE ccr\$r US€- tvt9 <{ \-}i ^' oZ \ ,/ i =*t .€ L = \lJNlt r 4 - l - I It*i) I I = \t 'lN J "H(,u*=.* [{rt}nenc\ srrcn = 3 [1Zt = s-[,,r .q4Gt;'' N L. -W( 7 1t b-.

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t tp rv =.*:: *'l ,r.;.1 ;N\ \6'fs ,1 h =T F =J I t-- x--{ | '*N hr L. r3A *- l*2!- rqnf*] b trr=.,,ra-ngl ffi--l TU h*fi er-i'{l l'c =t''i = @'vfu'ln' ?=z ____7 r}l I ,/\, 1 ao4-N , lr -ffi )[, r I r-: \rf.{ = tf .X h J t,l*NEtstr{. 1':t:!J t- u ' r / \ \l rz{'trl :Ti u\rd)u+lr-,\ il'?I F l\ttqf ' \ ' c - \ 1 \$ 3J- fN,.-tv"1 I_=t*f -r ffi [t r J r- = f N 'N? , N_ - , "t,* - ,- f.l I I t+Nf+ 6. n J € = L 1-- | . -\. t't" t(*Df* b+Nl€ = Lr*Df* h+ I N
z. (ro points each) Integrate )r(x.:5a ,{ osxs!!

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