Calculo diferencial e integral
Enviado por Javier2124 • 29 de Abril de 2019 • Exámen • 954 Palabras (4 Páginas) • 1.052 Visitas
CALCULO DIFERENCIAL E INTEGRAL
JAVIER ALTAMAR PEREIRA
ID 572139
UNIMINUTO
BARRANQUILLA
2017
ACTIVIDAD No.1
Ejercicios 5 – 1
1. Dada f(x) = 3x+ 2 calcule : f (1), f (-2), f (x2) y f (x+h)
f (1) = 3(1) +2 = 5
f (-2) = 3(-2) +2 = -4
f (x2) = 3 (x2) +2 = 3x2+2
f (x+h) = 3 (x+h) +2 = 3x+3h+2
2. Dada f (x) = 5 - 2x, calcule : f(3), f (-1), f(x), f(x+h)
f(3) = 5-2(3) = -1
f (-1) = 5-2(-1) = 5 (2) = 5 + 2 = 7
f(x) = 52(x) = 5 – 2x
f(x+h) = 5-2(x+h) = 5-2x-2h
3.f(t)=5t+7
f(1)=5(1)+7=12
f(-3)=5(-3)+7=-8
f(c) =5c+7
f(1+c)=5(1+c)+7=5+5c+7=12+5c
f(1)+fcc=(5(1)+7)+(5(c)+7)=12+5c+7=19+5c
4. f(x)=3-4x
f(a)=3-4a
f(a+1)=3-4(a+1)=3-4a-4=-1-4a
f(a)+f(1)=(3-4a)+(3-4(1))=3-4a-1=2-4a
5. f(x)=3 (x2+7
f(c)=3 c2+7
f(c+h)=3(c+h)2+7=3( c2+2ch+ h2)+7=3c2+ 6ch+ h2+7
f(c+h)-f(c)=(3(c+h)2+7)-( c2+7)
=3c2+6ch+ h2+7-3c2-7
= h2+6ch
6. Dada f ( x ) = 3x2 + 7, calcule: f ( c ), f ( c + h ), f ( c + h ) – f ( c )
f ( c ) = 3 ( c )2 + 7 = 9c + 7
f ( c + h ) = 3 (c + h )2 + 7 = 3 ( c + h ) 2 + 7 = 3c 2 + 3 h2 + 7
f ( c + h ) - f (c ) = (3c2 + 3h2 +7 ) + ( 3c2 +7 ) = 3c 2 + 3c6 3h2 + 7 – 3c2 + 7 = 6ch + 3h2
7 f(x)=3
f(1/x)=3
f(x2+)=3
f(x+2)=3
f(x+h)=3
8.f(y)=5
f(1/y)=5
f(y2)=5
f(y+3)=5
f(7)=5
f(y+h)=5
9.f(x)=√x
f(4)= √4=2
f(x2)= √ x2= x
f(a2+h2)= √a2+h2
10.f(x)=√x-16
f(25)=√25-16=√9 =3
f(0)= √0-16 =√-16= no existe
f(7)= √7-16 = √-9 = no existe
11. f(t)=3t2-5t+7
f(0)=3(0)2-5(0)+7=7
f(1/t)=3(1/t)2-5(1/t)+7=3/t2-5/t+7
f(c)+f(h)=(3c2-5c+7)+( 3h2-5h+7)
=3c2+3h2-5c-5h+17
12.f(u)= 2a2+3a-5
f(0)=2(0)2+3(0)-5=-5
f(1/x)= 2(1/x)2+3(1/x)-5=2/x2+3/x-5
f(x+h)=2(x+h)2+3(x+h)-5
=2(x2+2xh+h2)+3x+3h-5
=2x2+4xh+2h2+3x+3h-5
f(x+h)-f(x)=(2x2+4xh+2h2+3x+3h-5)-(3x2+3x-5)
=2x2+4xh+2h2+3x+3h-5-3x2-3x+5
=-x2+4xh+2h2+3h
13.f(x) 2X-3 si ≥ 5
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