Question

In: Math

Prove that: a) |sinx|<= |x| b) x = sin x has only one solution in real...

Prove that:

a) |sinx|<= |x|

b) x = sin x has only one solution in real number using mean value theorem

Solutions

Expert Solution


Related Solutions

prove that f(x)=x^2019 +x-1 has only one real root
prove that f(x)=x^2019 +x-1 has only one real root
Suppose that x is real number. Prove that x+1/x =2 if and only if x=1. Prove...
Suppose that x is real number. Prove that x+1/x =2 if and only if x=1. Prove that there does not exist a smallest positive real number. Is the result still true if we replace ”real number” with ”integer”? Suppose that x is a real number. Use either proof by contrapositive or proof by contradiction to show that x3 + 5x = 0 implies that x = 0.
a. Prove that y=sin(x) is a subspace of R^2 b. Prove that a set of 2x2...
a. Prove that y=sin(x) is a subspace of R^2 b. Prove that a set of 2x2 non invertible matrices a subspace of all 2x2 matrices
Prove by contradiction, every real solution of x3+x+3=0 is irrational.
Prove by contradiction, every real solution of x3+x+3=0 is irrational.
Find the general solution of the differential equations. A: cos(x)y′(x) + y(x) sin(x) = 0 B:...
Find the general solution of the differential equations. A: cos(x)y′(x) + y(x) sin(x) = 0 B: 2xy + (x2 + y2)y′ = 0 C: (4x3 +2xy2 +1)dx+(2x2y−1)dy=0. D: x(4x3 +2xy2 +1)dx+x(2x2y−1)dy=0 with steps please.
prove that 2/pi is less than or equal to (sinx)/x which is less than or equal...
prove that 2/pi is less than or equal to (sinx)/x which is less than or equal to 1. for x is in (0,pi/2]
Prove or disprove the statements: (a) If x is a real number such that |x +...
Prove or disprove the statements: (a) If x is a real number such that |x + 2| + |x| ≤ 1, then x 2 + 2x − 1 ≤ 2. (b) If x is a real number such that |x + 2| + |x| ≤ 2, then x 2 + 2x − 1 ≤ 2. (c) If x is a real number such that |x + 2| + |x| ≤ 3, then x 2 + 2x − 1 ≤ 2....
Differentiate. 1a) p(x) = 4th root of (2x-3/x^3) b) q(x)= (2 sinx)/(1-cosx) c)r(x)= sin(csc^3(x^4)) d) U(x)=...
Differentiate. 1a) p(x) = 4th root of (2x-3/x^3) b) q(x)= (2 sinx)/(1-cosx) c)r(x)= sin(csc^3(x^4)) d) U(x)= ((cube root of x^2) sinx -2x-3)/sq. rt. x
Real Analysis: Prove a subset of the Reals is compact if and only if it is...
Real Analysis: Prove a subset of the Reals is compact if and only if it is closed and bounded. In other words, the set of reals satisfies the Heine-Borel property.
1. Differentiate the following functions A. y=ln(x+sqrt(x^2 -1)) B. y=ln(sinx) C. y=xlnx-x D. y=e^x(sinx)
1. Differentiate the following functions A. y=ln(x+sqrt(x^2 -1)) B. y=ln(sinx) C. y=xlnx-x D. y=e^x(sinx)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT