Q3) Evaluate the following using simpson's rule; h=1 3 -5 x dx i sinx

Q: | sin(6y) sin(8y) dy.

A: we have to solve the integral

Q: 16. / cot(z) dr 17. cot (x) dr 18. csc(r) dr

A: (16) ∫cot(x)dx ∫cot(x)dx=∫cosxsinxdxPut t=sinx      dt=cosxdx we get-∫cot(x)dx=∫1tdt…

Q: QI: Drawing the Function Y = sin(x) X=0: pi/20 :2*pi and using the line of the color ( Magenta )…

A:

Q: i) S, 3 In dx.

A:

Q: wo iR fen) a Sin Cnuw) find E(7) E(7) - ?

A: In this question, the concept of Z-transform is applied. Z-transform In its most basic form, the…

Q: sinx?) fnd ds H.W

A: Given: To Find:

Q: T Use Trapezoid rule to approximate the value of sin xdx. 4 sản xuất 0

A: using h=pi/4 and formula for Trapezoid rule.  If you change h you will different answer. You can…

Q: 6. S sin2xdr sin'r-4

A: We will use partial fraction to solve th integration after substitution. Which is as follows

Q: xsin dx V1-x? 1/2 : Evaluate : x sinx

A:

Q: i) S, (x Inx)³ dx. ii) S •1 3 In) dx.

A:

Q: 15. S Vx sin?x³/2 dx.

A:

Q: S(csc?x - cot?x + sec 2x) dx Evaluate

A: Given,  ∫csc2 x-cot2 x+sec 2xdx

Q: Simplify the equation: sechx + sinhx tanhx cosh z cosh a sechx 1+ sinh 2 cosh z

A:

Q: T 3 x* sin (x) dx 3

A:

Q: 1 + sin² (x) dx sint(x)cos (x)

A: We have to find the integral.

Q: 9.f tan3³ x √sec x dx

A:

Q: Differentiate the given function. y=XV8X-5 y'= (Type an exact answer, using radicals as needed.)

A:

Q: Use the general form of Parseval's equality to show that i sin w (sin(w +2) dw = 0. w + 2

A: To Show : Use the general form of Parseval's equality to show that  ∫-∞∞sinωωsinω + 2ω + 2dω = 0

Q: | tan° xsec* xdx 6 2. Use 1 + tan² x = sec? x to evaluate

A: Solution:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.