Vx4 + 39x + 13 – 4 = 0

Q: (c) Prove the inequality I +y +x > Vryz 3 if x > 0, y >0 and z > 0.

A:

Q: 2. Solve and state the largest interval over which the general solution is defined: dy (x+ 2)´ Jr =…

A: Answer

Q: At what interval is y=3x- 5x3 concave upward? 2 2. <x<0 U x) 21 2. U 0<x< U0<x<

A:

Q: At what interval is y=2x4-4x2 concave upward? 3 3 3. V V V

A:

Q: Given that z ∈ C where |z| = 1 , solve for : |1 + z|2 + |1 - z|2

A:

Q: Determine the intervals in which solutions are sure to exist. t(t − 2)y(4) + e¹y" + 6t²y = 0 Enter…

A: As per the question we are given a forth order linear differential equation as : t(t-2)y(4) + ety''…

Q: find the solution to the Cauchy-Euler equation on the interval (0,∞). In each case,m and k are…

A: Since we have to find the Cauchy-Euler equation, we will substitute y=xm which will yield…

Q: for which the sys y +z = 6, 4x + Ay = -5 has infinitely m a root of which qu: %D :

A:

Q: Let y(x) be the solution for the DE : y = (x + y – 1)2 If y(0) = 1, thenfind y(4)

A:

Q: The solution of the IVP t(t + 4)y + (t + 4) y= t, y(2) =2 exists in the interval

A: In the question it is asked to solve the initial value problem as shown below. t(t+4)y'+(t+4)y=t2…

Q: state where in the ty-plane the hypotheses of Theorem are satisfied 7. y′=(t2+y2)3/2

A: Given y'=t2+y232

Q: By the Existence and Uniqueness Theorem, the IVP y' + y = sin x x2 – 25' y(3) = 0 is guaranteed to…

A:

Q: The functions f(a)= 7e and f(2)= 22" form a fundamental set of solutions of the DE on the interval…

A: The function f1x=7x and f2x=2x3 form a fundamental set of solution of the differential equation…

Q: 1. Find the interval(s) wheref(x) = xe6* is concave down, if such an interval exists.

A:

Q: Use the Intermediate Value Theorem to show that the following equation has at least one nonzero…

A: Given That,  Sec(2x)= 3^x

Q: The approximation to a root of the equation x^2+x-1=0 in the interval [0,1] b applying the regula…

A: The given equation is x2+x-1=0  find the value of f(0) and f(1)  fx=x2+x-1f0=02+0-1=-1…

Q: Prove that the following equation has no natural solutions x? + x +1 = y².

A: we have to prove that given equation has no natural solution

Q: (e) f(x1,x2) = xỉ/x2 on R x R++.

A: The solution of (e) is in below

Q: Find values a, b, c, d such that the function (x+ 1)³, -2 < r <-1 s(x) = { ar³ + bæ² + cx + d, -1 <…

A:

Q: he IVP d's (p² – 121) dp1 d's ds + s 1 = sin(p) dp3 p2 +1 dp s(7) = -994 ds = 19 dp l7 d's = 4 dp2…

A: Given the IVF (p2-121)d4sdp4+p4d3sdp3+1p2+1dsdp+s = sin(p)s(7)=-994[dsdp]7=19[d2sdp2]7=4[d3sdp3]7=10…

Q: y" — 5y' = x − 2, when x = 0, y = 0, y' = 2

A: To find the particular solution for the given DE.y''-5y'=x-2, when x=0, y=0, y'=2

Q: Let f(z) =z² – 40, g(z) = 3z – 5. Solve for z exactly: f9(=}) = 0

A:

Q: Use the method of separation of variables to solve: - = 0 in (0,1)×(0,+∞), at? ôx (1) u(0,t) = u(1,…

A:

Q: Prove that c?p?-(jx² + jy²+jz³) is the invariant quantity equal to c?po?.

A: Consider the provided question,   Prove that c2ρ2-jx2+jy2+jz2 is the invariant quantity equal to…

Q: Solve the following Cauchy problem: -00 0, u(r,0) =r-r, (x,0) 4r, -x <r<x.

A:

Q: Determine the interval in which solutions are sure to exist. y(4) + 6y" + 3y = t %3D Valid on the…

A:

Q: Suppose v(t) = 6t² - 3t on the interval [3, 5]. What is the displacement on [3, 5]? O 160 O 165 O…

A:

Q: Find the solution of the PDE t> 0, x = [0, π] x= [0, π] √u₁-ux = U₂ [u(x,0) = 3 senx + sen3x,

A:

Q: Determine the interval in which solutions are sure to exist. y(4) + 7y" + 6y = t Valid on the…

A: Given differential equation is y4+7y'''+6y=t. We have to determine the interval in which solutions…

Q: * السؤال The largest interval for which the IVP: (In(e* – e²)) y' + y = 1, y(5) = 0 has a unique…

A:

Q: Solve the given IVP for the Cauchy-Euler DEQ t²y"(t) – 4ty'(t)+ 4y(t) = 0; y(1) = –2, y'(1) = -11…

A:

Q: 1 f f(x) = : R → R, Vx2 – 4 At how many different integer points x is discontinuous? 25 - O A) 3 O…

A: We have f(x) = 1x2-4Clearly f(x) assumes real values for all real values for all x except for the…

Q: ニメ Find the eg uaton (x) 4a| %3D 3tan x when fo f the tor

A:

Q: Exercise 9: For the following, use the intermediate value theorem to prove that the given equations…

A: a) The given equation is

Q: The function U(x, y) satisfies the equation a²U_a?U + ax2 ' ay2 = -2, at every point inside the…

A:

Q: Find positive numbers x and y satisfying the equation xy = 16 such that the sum 2x+ y is as small as…

A:

Q: Verify that y = c₁ex + c₂e4x is a solution to the DE: y" - 5y + 4y = 0.

A: We are authorized to answer one question at a time, so we are answering the first one, please repost…

Q: Match the exропent equality to the correсt solution for x. 1. 27*-3 3* а. х — —4 2. 5-5 = 5 b. х — —…

A:

Q: 2ste-tds + (s²e-t – t)dt = 0

A:

Q: Prove that the equation Z = 1 has no ++ solutions in positive integers x » Y, Z.

A: Assume some value and substitute it many times taking different domains like integers, whole numbers…

Q: Let z = x(1 – i) + 8(-2+ i), where x is a real number. If z? is a negative real %3D number, what is…

A: Given, z=x(1-i)+8(-2+i) and z2 is a negative real  number. We have to find the value of x

Q: Solve the second-order DE y"+2y'+4y= g(1), y(0)= 0, y'(0)=1, where 2, Ost<2 g(1) ={-2, 2si<4 0, 124.

A:

Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.

Q: Find two consecutive integers m and n such that a solution to f(x)=0 is in the interval (m, n),…

A:

Q: Show that Y, CX) = x is one of this functio %3D Solutions: x*y" + 2 xy' - 2 = 0

A:

Q: Use the intermediate value theorem to show that the equation x^3+x^2−2x+1=0 has a solution i the…

A: (note - I assume i as iota) f(x) = x3+x2-2x+1 At x= -1,      f(-1) = (-1)3+(-1)2 -2(-1) +1…

Q: Find the are length of f(r) = (r + 3)2 from r = 0 to x = c in terms of c. %3D 2/3

A:

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.