If C: r(t), t  ∈ [a,b], a regular curve at R cuved, oriented from the ponit P=r(a), to the point Q=r(b). If z is different to 0, the integral (photo1.0) can be calculated with the integral fundametal theorem using the line? (photo 1.2)

Q: Derive the De Moivre's Theorem with detail Explanation?

A: Statement: For any real number x, we have (cos x + i sin x)n= cos(nx)  i sin(nx) Or, (eiθ)n=eiθn…

Q: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

Q: part öf the cicle42| = 2 in the first quadrant. Find an upper bound for the integral . b) Let C be…

A: Solution-(a) the path of integration has the length L=4π Upper bound M for the function =1z2+1;z=2…

Q: The arc of the parabola y =  x sq.  from ( 1,1, )  to ( 2, 4 )  is rotated aboutthe  y -axis. Find…

A: Given:The arc of the parabola y=x2 is rotated about the y-axis from 1,1 to 2,4. We have to find the…

Q: we draw a tangent line on y=/25 –x² at x = -3. 14 - find the slope of this tangent line. O A) 2/3…

A: To find- slope of the tangent line.

Q: Q3 Check the symmetry and graph the curve in polar form if 0 = 0 and equal 1/6 to 1/2 at increments…

A:

Q: Find an equation of the tangent plane to the graph of F(r, s) at t F(r. s). - (3r4 1 + 1), (-1, 1.…

A: Introduction: Let z=f(x,y) denote the equation of a surface S in R3, and P=(a,b,c) denotes a point…

Q: Let f(x, y) = 5ex - Y. Find the equation for the tangent plane to the graph of f at the point (5,…

A: Given: fx, y=5ex-y. To Find: Equation of tangent plane to the graph of f at the point 5, 5.

Q: Find the D.E. for each of the curves determined by the condition that at each point (x, y) ,   The…

A:

Q: -dz Q5/ (A) Find the value of the integral 3 where C is the circle z+2 = z(z+1)"*1

A:

Q: find enclosed by following curves area Oくx(2て (a) 4= Cog x ;y=2- Cosx ; (b) y = X Sitx? Recall…

A: (a) y=cos(x), y=2-cos(x) Lets graph both equations using graphing calculator Area =∫abupper…

Q: Prove that there no line through the point (0,1) is tangent to the graph of y = x*.

A:

Q: Find an equation of the tangent plane to: 3x +y = z at P(-1,1,-2) %3D

A:

Q: Consider the folloinwg curve: y = square root of -1+2x At what point on the given curve is the…

A: Consider the folloinwg curve: y = square root of( -1+2x) to find the point on the given curve is the…

Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

A:

Q: Write the equation of the curve l_r(t) which traces the circle of radius (0,0,1) on the plane z=1.…

A:

Q: At the point (a, b) the curve T =t-4t, y=t2 +2t, t eR has a vertical tangent line. What is the sum a…

A:

Q: The tangent to the curve f(x) = V9 – x² at the point where x = B makes an angle of 30° measured with…

A: Using the Slope of tangent =dy/dx. and slope of tangent = tan(@)

Q: Exercise 1. A student is asked to prove If m is even and n is odd, then m² + n² is odd. 2 The…

A: Let us answer above questions

Q: Evaluate the integral xy ds, where C is the curve consisting of the portion of the unit circle of…

A: The given integral is ∫Cxy ds where C is the curve consisting of the portion of the unit circle…

Q: Tangents are drawn to x² + y² = 1 from any arbitrary point P on the line 2x + y - 4 = 0. The…

A: Tangents are drawn to x2+y2=1 from any arbitrary point P on the line 2x+y−4=0. We have to find the…

Q: Show that th equation of the tangent to the curve X 1승 +1-2(a 0,b + 0) at the point (a,.b) is 즈+-2 X…

A:

Q: Let y = f(x) be defined parametrically as y = f + as y=t+tt, x = 2t -tl, te R. Find f(x) and discuss…

A: