Cauchy integral Formula and problems
Trending Questions
The domain of the function is . Then a is equal to:
- 2πi
- −πi/2
- −3πi/2
- π2i
- 0
- 2π
- 2π√−1
- α
Find the range of function .
Let and be three sets defined as . Then the set
Has infinitely many elements
Has exactly two elements
Has exactly three elements
Is a singleton
The area bounded by the curves and is
square units
square units
square units
None of these
- −πsin(1)/e
- −πcos(1)/e
- sin(1)/e
- cos(1)/e
The domain of the function is
- 0
- 1/10
- 4/5
- 1
Let is not differentiable at . Then the set is equal to:
an empty set
Let the function : be defined by and let: be an arbitrary function. Let be the product function defined by . Then which of the following statements is/are TRUE?
If is continuous at , then is differentiable at
If is differentiable at , then is continuous at
If is differentiable at , then is differentiable at
If is differentiable at , then is differentiable at
If C denotes the counterclockwise unit circle, the value of the contour integral 12πj∮CRezdz is
- 0.5
The value of the integral 12πj∮Cz2+1z2−1dz where z is a complex number and C is a unit circle with center at 1+0j in the complex plane is
- 1
- 1
- 2
- 0
- −1
where c is the rectangular region defined by z=0, x=4, y=−1 and y=1
- 1
- 0
- π2i
- π(3+2i)
The derivative of is
In the following integral, th contour C encloses the points 2πj and −2πj.
−12π∮Csinz(z−2πj)3dz
The value of the integral is
- 133.87
The angle between the curves and at the point other than the origin is
- −0.511−1.57i
- −0.511+1.57i
- 0.511−1.57i
- 0.511+1.57i
The correct Γ is
If C is defined as |z|=3, then the value of I is
- −πisin(1)
- −2πisin(1)
- −3πisin(1)
- −4πisin(1)
Let be defined as:
If is continuous on , then equals to:
- πi2
- 2πi
- −πi2
- −2πi
- 0
- 2πj
- α
- 12πj
The contour C given below is on the complex plane z=x+iy, where j=√−1.
The value of the integral 1πj∮Cdzz2−1 is
- 2
- −2
- −1
- 1
- 2
The coefficient of correlation between two variable and is given by
- −2πi
- 0
- −2πi
- 4πi
- I=0, singularities set =ϕ
- I=0, singularties set ={±2n+12π;n=0, 1, 2}
- I=π2, singulariteis set =±nπ;n=0, 1, 2...
- None of the abvoe
- −4π(1+j2)
- 4π(3+j2)
- −4π(3+j2)
- 4π(1−j2)