Quiz

proof

1.  Which of the followings represents the sum of purple area demonstrated in the picture to the right?

  • 1+ 1 4 + 1 16 + 1 64 +... MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiabgU caRmaalaaabaGaaGymaaqaaiaaisdaaaGaey4kaSYaaSaaaeaacaaI XaaabaGaaGymaiaaiAdaaaGaey4kaSYaaSaaaeaacaaIXaaabaGaaG OnaiaaisdaaaGaey4kaSIaaiOlaiaac6cacaGGUaaaaa@4268@

  • 1 4 + 1 16 + 1 64 +... MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGinaaaacqGHRaWkdaWcaaqaaiaaigdaaeaacaaIXaGa aGOnaaaacqGHRaWkdaWcaaqaaiaaigdaaeaacaaI2aGaaGinaaaacq GHRaWkcaGGUaGaaiOlaiaac6caaaa@40CB@

  • 1+ 1 2 + 1 4 + 1 8 +... MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiabgU caRmaalaaabaGaaGymaaqaaiaaikdaaaGaey4kaSYaaSaaaeaacaaI XaaabaGaaGinaaaacqGHRaWkdaWcaaqaaiaaigdaaeaacaaI4aaaai abgUcaRiaac6cacaGGUaGaaiOlaaaa@40ED@

  • 1 2 + 1 4 + 1 8 +... MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGOmaaaacqGHRaWkdaWcaaqaaiaaigdaaeaacaaI0aaa aiabgUcaRmaalaaabaGaaGymaaqaaiaaiIdaaaGaey4kaSIaaiOlai aac6cacaGGUaaaaa@3F50@

proof

2.   According to Archimedes' Method of Exhaustion, which one of the following gives the area of the paraboloic segment in terms of the blue triangle T.

  • 4 3 T MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aI0aaabaGaaG4maaaacaWGubaaaa@385B@

  • 3 2 T MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIZaaabaGaaGOmaaaacaWGubaaaa@3859@

  • T

3. Archimedes is regarded as the father of Integral Calculus. True or False?

  • True
  • False

4. What type of series does Archimedes' method of exhaustion refer?

  • Arithmetic Series
  • Geometric Series
  • None of the above