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Q: Show that the functions have exactly one zero inthe given interval. g(t) = 2t + √1 + t - 4, (0, ∞)

A: g(t) = 2t + √1 + t - 4,              x ∈ (0, ∞)    g(t) = 2t + √(1 + t)  -  4

Q: If m s f(x) < M for a s x s b, where m is the absolute minimum and M is the absolute maximum of f on…

A: ∫0421+x2dx

Q: Supose z is implicitly dofimed by the equation qy+ 3x + XyZ + 32=9 in an onvanment of the point…

A:

Q: The weenay demand for petroeum of a 1ocal gas stanion in thourana itens ie given by: flo) = 48 ( x-)…

A: Given: X is the demand of gas per week in 000 fx=48×x-0.51-x    0.5&lt;x&lt;1

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 &amp; x=2rcos θ , y=2rsin θ

Q: 30. Find the continuous function f(t) satisfying csin z for all r. 2+ f(t)dt = sin2015 /3

A: According to Leibnitz rule:

Q: Find an upper bound for ||L|| where L: R² → R³ with L(x, y) = (2x + y,x + 3y, 3x – 2y) -

A: Here we use the definition of boundedness of a linear operator.

Q: Find the linearization of the function f (x) = x at a = 1. a Va lal sin (a) L (1) Using this…

A:

Q: we have (x-Z) + y? < 1 2. function: F = x²+ Y2 and location of absolute Find value maximum and…

A:

Q: Assume x and y are functions of t. Evaluate dx = 9, x = 3, y = 0. for 4xe = 12 - In 729 + 6ln x,…

A: Given query is to find indicated derivative.

Q: Q.2 - Use the Riemann sum approximations to approximate the area under the curve of y = x on the…

A:

Q: Let z = cosh t. Find the differential dz when t = In 3 and dt = 0.2 O 4/3 O 4/15 O 8/15 O 1/3

A:

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y=2rsinė

A: this is a problem of differential. Based on the general formula and concepts we will answer the…

Q: If m s f(x) s M for a s x s b, where m is the absolute minimum and M is the absolute maximum of f on…

A:

Q: If m s f(x) SM for a s x s b, wherem is the absolute minimum and M is the absolute maximum of f on…

A:

Q: Q2: Expand f(x,y) = [sin (x y³)]² about (5, 1).

A:

Q: Evaluate lim (csc a) V. x0+ Let f(x) = Va + le¬*. 1. Find the local linear approximation of f at xo…

A:

Q: Let f(x, y) = ay + 1. Find the absolute maximum value and the absolute minimum value of f(r, y) on…

A:

Q: The density of seeds at a distance x from a parent tree is observed to be -x2 = Doe a2 %3D where a >…

A: In the given question, the concept of maxima and minima is applied. Maxima and Minima The critical…

Q: Ex filnd divergenceof f when yj at (o1). 2 e ( + 9 J

A: See the answer below

Q: 5. (a) If f(x) = x · 2“, give an estimate of the net area of the region bounded by fand the x-axis…

A: As you post multiple question according to guideline i only solve first part. please post the other…

Q: Find the limit of function f (x, y)D. at the point (0,0) through the path x=y². а. О b. 1 8 d. does…

A:

Q: Is xo is an ordinary point of the ODE? If so expand p Find a minimum value for the radius of…

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Q: Eliminate the arbitrary constants a. x = -In t, y = at + bt?

A:

Q: 1 Find the local linear approximation of f(x) = , at 3+ 1 Tg = 2, where Az = I- 2. NOTE: Enter the…

A:

Q: > Approximate o using the trapezoidal Rule x² dx Is this an wnderestmahon or over estimation ?

A: we have been given the function f(x)=x2

Q: (b) Show that the roots of y'(x) = 0 are x = 0, x = L, and x = L/2, so it follows (why?) that the…

A:

Q: Let I = W/H^2 denote the BMI. Estimate the change in height that will decrease I by 1 if(W,H) = (25,…

A: I = WH2    (Given)    W=26                         H=1.1   W= Constant (given) I = WH2 = W(H2)-1 =…

Q: Q10. Expand f (x, y) = e" cosx about up to third degree terms by using Taylor's theorem for a…

A: The given problem is to find the third degree taylor polynomial of given function f(x,y) about point…

Q: Find the zeYo k its ovdev for Sunction f2)=1-Ti + Z+ e.

A: Given the function, f(z)=1-πi+z+ez. Now, in order to find the zero of the function f(z), we will…

Q: of Let f (x, y) = tanh-¹(x-y) with x=e" and y= usinh (t). Then the value of dt (u,t) =(4, In 2) is…

A:

Q: Suppose ƒ is differentiable on (- ∞, ∞), ƒ(1) = 2, and ƒ'(1) = 3.Find the linear approximation to ƒ…

A: Given that,  Function f is differentiable on (−∞,∞), f(1)=2, and f'(1)=3. The linearization of f at…

Q: Q4: integrate the following function f(x,y) for x from z to 2n and for y from 0 to f (x, y)=…

A:

Q: fhow thot te function f depined by f(XrY) = 1 (x,Y) =(1,-リ - 1) %3D x2 +y (x, y) F (I,-1) * t y is…

A: We use the sequential definition of continuity to solve this problem.

Q: The graph of a differentiable function f on the ir [2,10] is shown. Find the trapezoidal approximat…

A:

Q: التاريخ الموضوع Find The approximate value of f(x) at X=1-2 whereof is defined over The period 1.7]…

A: The given table is To find: f(1.2)

Q: If m s f(x) s M for a sxs b, where m is the absolute minimum and M is the absolute maximum of f on…

A:

Q: Let T, be the approximation using n subintervals for the Trapezoidal rule to estimate I =…

A:

Q: V Sove using variaton of parameters recuction of order or (D² - 2D+1) y = e*(e*+)*

A: Please find attachment for the details solution

Q: ) Fnl the Vdume of the Selid enclesed by the curres "about the x-axS. y=e^, y=0 x =©,'x=/

A: To find out the volume of solid of revolution.

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) = 1 a = 3 L(x) :…

A: The solution are next step

Q: If m < f(X) < M for a < x s b, wherem is the absolute minimum and M is the absolute maximum of f on…

A:

Q: Evaluate in terms of Gamma function: y^5√(b^2 – y^2) dy LIMIT: 0 to b

A: The given data is: y5b2-y2 dy limit is 0 to b To evaluate in terms of Gamma function.

Q: Suppose f(z) = 1 + sinz and F is an antiderivative of f that satisfies F(띠) =D0. Then F(z) = - COSX…

A: Integrating f(x).

Q: Show that the p.d.f. of Z is given by g1(r) = e-1(+A)cosh(vAx), x > 0, where cosh(2) = }(e² +e=*) is…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: Is e^z differentiable? O a. Yes O b. No O c.Not at all O d. all of the above

A:

Q: if f(x)=integral t^3+5t^2+6, from 0 to x. what is f''(x)=?

A:

Q: Find the 2nd solution using reduction of order. xy" +y' = 0; y1 = Inx For the toolbar, press ALT+F10…

A: Just I have used the method of reduction of order and solve in detail and find that  Second solution…

Q: Q6) Find the approximate value of A and B in ya = x(1-x)(A + Bx) where y + x² = 0 and y(0) = y(1) =…

A: Given differential equation with condition is y''+x2=0, y(0)=y(1)=0 Given approximate solution is…