2uppore that tuo - dimensional, contiruous Mandom uariable (x,4) fa's yont" P•d.«b. gien by : , elsewhere us woify trat c ind P (o

Q: 13. The range of the arcsin or sin(x) is: a) (0, 2.7) b)(0, 7 ) ) 0. d) 4 '4 e) 2'2 4

A: 13) Given

Q: Q Find the derivativeof y)with respect tox; in the foltowina function s and u=3X 2 Find dy for the…

A: Given that  The functions  As for the guide lines to solve the one question but here I am solving…

Q: 1 2 #5) A) Find the length of a curve y Inx for 3 < x < 7. 4

A: L= integration of sqrt of 1+ (dy/dx)2 dx from a to b

Q: In each of the Convemence and interval of Comvergent fellowing, find the radıus af (2) (2n)! incn+2)

A: 3) The series is given as ∑xn(2n)! Let an = xn(2n)!an+1 = xn+1(2(n+1))! Consider limn→∞an+1an =…

Q: 13. Prove that dx ≤ f √√√x x+1 2 1/7/3 (Hint: use Cauchy-Schwarz)

A: Given:∫02xx+1dx≤23

Q: Without solving , determine the interval of existence for the following I.V.P (x² – 4) y" +2- 3 y'…

A:

Q: 18. 19. The curve y = x³ – 3x² + 2 has an inflection point at the point: a) P(1, 0) b) P(-1, -2) c)…

A: 18) Given that : We  have  to  find  the  point  of inflection of the  given…

Q: 2 question Jet flz)= (7-1)sinllx-1)²+2y2) for fl)=0 ond 3= x + iy e ¢\ {13. a) Show that the…

A: fz=z¯-1sin(x-1)2+2y2z-12f1=0 and z=x+iy∈ℂ\1To show that: f is continuous at point z0 =1 and f has no…

Q: 6) a) show that Sx dx is divergent b) Show that Lim = 0. This shows we canuat xdx -- define = im…

A:

Q: Since the tangent equation of f(x) = x^3 – x^2 + 3x – 5 drawn from the x = 1 apse point on it is y =…

A: Given : Function  f(x) = x3 – x2 + 3x – 5 Tangent equation on the given function f(x) at point x =…

Q: if the tangent tangent (x117₁) to the conve of the curve again in (22, 8₂) them proustait me x 1 20…

A:

Q: The first derivative of the function y = 4*.32x is: %3D a) 4*.6* In 36 b) 4*.32x In 4 + 4*6* In 6 c)…

A: given y=4x.32x

Q: is homeomorphic to R, where f (x) = tan¬1 x. 2'2 1) Check

A: Given: The function is fx=tan-1x To check: The map (-π2,π2)→R is a homeomorphic.

Q: How would you remove the dis . z46 f(r) =

A:

Q: Could you continue solving this problem using  applied analysis.

A: The objective of the question is to estimate the interval of existence for the given initial value…

Q: #4) What valwes of c Cif anu) are predicted by the Me an Vae Thearem for the function fex) = (x-32)o…

A: The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and…

Q: The curves y = In x and y = 3x² have parallel tangent lines at x = A) ± √/ B) C) √6 E) 2

A: Two lines have parallel tangent if slop at the point is same.

Q: Question 3. the interval(s): a) (-00, 00) b) (-0, -) and (, +0) c) Nowhere (it's always con- cave…

A: Given function is f(x) = e-x2

Q: s=2 caslzt)- Sin S) 7ズ ds Ty pe as eaCkt amw sr usin

A: In this question We want to differentiate s with respect to t.

Q: Sketch the level curves of the function f(x, y) = = I x+y for c= -6.

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: The graph of y = 2x1/3 + x4/3 changes its concavity at: 1) nowhere 2) both (0,0) and (1,3) 3) (0,0)…

A:

Q: Find the values of a and b so that f will be differentiable at x = 3.

A:

Q: show that f in Vienann and findit Limibs 2. 0 FC)= X 2) fCX) = -X? iXE [011] XEE-li0] %3D %3D

A: (1) fx=x2 , x∈-1,0 ∫abfxdx=∆xfx0+fx1+fx2+......+fxn-1 Where ∆x=b-an we have that a=-1,b=0,n=4 ∆x=14…

Q: 63. Prove a famous result of Archimedes (generalizing Exercise 62): For r < s, the area of the…

A:

Q: Let/(x)=sin³ x+A sin² X

A:

Q: If f" CQ) = xa (x+)S (x-!) And all inflection points.

A: I have appended the concept used in the solution part

Q: Let f(x) = |r|. The derivative of f at a = 0: Question 1. a) Equals to +1 b) There are infinite…

A:

Q: If fuf fuare difla Veubableat XoeI n prove thacd Cfisfa fu) isclifferantiable at vo aucde.

A: