dv Prove that 4u/2n

Q: Evaluate the integral. 2 dt 1- t2 V

A:

Q: b 1+ e2x Evaluate the integral. ex xp 1 + e2x

A: Given that: ∫01ex1+e2xdx

Q: .rdx dy Prove that (a) (b) (8)

A:

Q: Evaluate the integral. 1 2 dt t2 + 1

A:

Q: Prove that X Pn dx %3D

A: Recurrence relation.  Partial fraction.

Q: 6. Find the integral Ssin T* jsin² 2 TTX 2.

A: We have to find integral

Q: Lw(s) ~ 1 – Show that 1 is MTTF where

A:

Q: dy is If y = In then cosh z

A: Given,          y=lnxcoshx

Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

A:

Q: 5. Use geometry to evaluate (V4- x² dx 2 O 2n O 4t

A: Solution:

Q: Evaluate the integral.

A:

Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: Evaluate the integral. +1 dt Vi 0.

A:

Q: 10. Find the integral| dt. t* +81

A:

Q: 1)z = e(4+j3) In(6230") 2) z = (-;)(* 2) z = (-)(r)"

A: (1) The  given complex equation is                                                Z=e4+j3ln6∠30°

Q: Evaluate the integral. dt V 4 + t2

A:

Q: 2) Prove that: d? L„0) = n;(n – 1) %3D dx²

A: Consider the given information: Let Laguerre polynomial is given by, Lnx=∑k=0n(-1)kk!nkxk…

Q: dx . Evaluate the given integral: S xV5x2-4

A:

Q: o prove that knVA=| Test the seuence (ConViordív) of (10) an = (^_-) ) an 15 ら 9n: 3ntl 3n-1 (の+ (7)…

A:

Q: S 1.Prove that L (coswt): %| s2 +w2

A:

Q: Prove that E (2s+l)=3n" whenever 'nisa psitre r'nisa pisitive intger. 32.

A: Given that,      ∑j=n2n-12j+1=3n2, n is a positive integer

Q: Find the integral. e3t dt Vest - 3 %3D 1

A:

Q: 2.Prove that L (sinwt) %3D s2+w?

A:

Q: Evaluate the integral. 1 cos 2t dt 2 7x/2

A: To evaluate the given integral.

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where u> |z| > 0

A: Prove,∫z=1dzz2 sinh z=-πi3 ∫z=1dzz2 sinh z=∫z=1fz dz .........equation 1 fz=1z2 sinh z , 0<z<π…

Q: (b) Evaluate the integral fxIn x dx using by parts formula.

A: Answer is:  (x2/2)lnx -x2/4 + C

Q: Evaluate the integral: 2e π/3 √√²² √²/³ t Inutans ds du dt

A:

Q: Consider the integral 2 6z² In(z) dz

A:

Q: Evaluate: (2x + 1)3 dx by two methods: 11) let u = 2x + 1 %3D 12) Expand (2x + 1)³ Compare the…

A: Integration

Q: 10. Using the substitution u 2x - 1, prove that %3D 3 8 dx J1 (2x-1) 25

A:

Q: 7. a) Prove that for r > 0 * (E) + c. Vr2 – r²dx = vr² – x² + -1 sin 2 +C.

A: To prove: ∫r2-x2dx=x2r2-x2+r22sin-1xr+C

Q: per integral test, (-1)" A) Σ B) none of these en (-1)" dz behaves like

A:

Q: Evaluate the integral. 2 2 t+ dt 15 OA. 29 О В. 6

A:

Q: 3. ncnt) use PMI to prove that E

A:

Q: Evaluate the integral. r3 3 cosh(t) dt 30.05

A:

Q: e In (x le) (2- secx dx to be integrable using the formula - se What should be the value of A for u"…

A:

Q: d 1 Prove that: dz (tan¬1 z) = 1+z?

A: Given query is to find the derivative of the expression.

Q: ZH E LI and HI 1 GJ. Complete the proof that AGIJ S AGHJ.

A: Here we use two concepts  1) sides opposite to equal angles of a.         triangle are equal. 2)…

Q: [4] 5. Use the fact that 1 +C 4e2r dx = 2e2 to either evaluate the improper integral 2 dr, or show…

A:

Q: Evaluate the integral. 1 8 dt V15-21-? - 1 OA. 6 В. O C. 4 D. 3" O D. co fm

A:

Q: 3t e"dt 2 (1+4e3

A: Let's integrate.

Q: Evaluate the integral. 2 [ 11t sec-'t dt 2/√√3 2 S 11t sect dt = [ 2/√√3 (Type an exact answer,…

A:

Q: dx Evaluate the integral: 3/2 64 -

A: To solve the given integral problem.

Q: D Find a singular saluhion of DE: %3D

A:

Q: 2 Evaluate the definite integral Зх + 4 dx 11 5 17 17 2 ךי" יזנ 3.

A:

Q: prove that d/dx xn=nxn-1

A: To proveddxxn=nxn-1

Q: Evaluate the integral. 7e 7t dt 7t 3+ e'

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.