Intermediate Value Theorem | Definition, Proof & Examples
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Intermediate Value Theorem | Definition, Proof & Examples
Understand intermediate value theorem and see intermediate value theorem proof. Practice intermediate value theorem examples to learn about its misreading and uses.
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SOLVED:Use the Intermediate Value Theorem to show that the function has a root in the indicated interval. (a) f(x)=3-x-sinx ;[2,3] (b) g(x)=3 x^4-2 x^3-3 x 2 ;[0,1] (c) g(x)=3 x^4-2 x^3-3 x 2 ;[0,0.9] [s] (d) h(x)=10-cosh(x) ;[-3,-2] (e) f(t)=√(4 5 sint)-2.5 ;[-6,-5] (f) g(t)=(3 t^2 tant)/(1-t^2) ;[21.5,22.5] [5] (g) h(t)=ln(3 sint)-(3 t)/(5) ;[1,2] (h) f(r)=e^sinr-r ;[-20,20] (i) g(r)=sin(e^r) r ;[-3,3] (j) h(r)=2^sinr-3^cosr ;[1,3]
SOLVED:Use the Intermediate Value Theorem to show that the function has a root in the indicated interval. (a) f(x)=3-x-sinx ;[2,3] (b) g(x)=3 x^4-2 x^3-3 x 2 ;[0,1] (c) g(x)=3 x^4-2 x^3-3 x 2 ;[0,0.9] [s] (d) h(x)=10-cosh(x) ;[-3,-2] (e) f(t)=√(4 5 sint)-2.5 ;[-6,-5] (f) g(t)=(3 t^2 tant)/(1-t^2) ;[21.5,22.5] [5] (g) h(t)=ln(3 sint)-(3 t)/(5) ;[1,2] (h) f(r)=e^sinr-r ;[-20,20] (i) g(r)=sin(e^r) r ;[-3,3] (j) h(r)=2^sinr-3^cosr ;[1,3]
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SOLVED:Use the Intermediate Value Theorem to show that the function has a root in the indicated interval. (a) f(x)=3-x-sinx ;[2,3] (b) g(x)=3 x^4-2 x^3-3 x 2 ;[0,1] (c) g(x)=3 x^4-2 x^3-3 x 2 ;[0,0.9] [s] (d) h(x)=10-cosh(x) ;[-3,-2] (e) f(t)=√(4 5 sint)-2.5 ;[-6,-5] (f) g(t)=(3 t^2 tant)/(1-t^2) ;[21.5,22.5] [5] (g) h(t)=ln(3 sint)-(3 t)/(5) ;[1,2] (h) f(r)=e^sinr-r ;[-20,20] (i) g(r)=sin(e^r) r ;[-3,3] (j) h(r)=2^sinr-3^cosr ;[1,3]
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