a e d b C

Q: The variable a is the length of the ladder. The variable h is the height of the ladder's top at time…

A: Using the Pythagoras theorem  a2=h2+x2x2=a2-h2 differentiate with respect to t Therefore…

Q: SOLVE IN HAND WRITTEN   Find the equation of the line if it passes through the points: (5, −1) and…

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Q: 7. Find the exact x-value where the function f(x) = x + ln (x² − 1) attains a maximum value. An…

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Q: Let f: RR be a function satisfying f(x + y) = f(x) + f(y) for all x, ye R. If the function f(x) is…

A: Note :   Let r>0 and c∈R ,then vr(c)={x∈R : x-c<r }=(c-r ,c+r) ,which is called r…

Q: A model for a certain population P(t) is given by the initial value problem

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: Let n € N with n > 2 and let G₁ = (V, E) be the graph with vertex set V = {₁, V2, ..., V2n} and edge…

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Q: Show that the polynomial ring Z4 [x] over the ring Z₁ is infinite, but Z₁ [x] is of finite…

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Q: Let f be a given function. A graphical interpretation of the 2-point backward difference formula for…

A: The 2-point Backward Difference Formula for approximating f'x is given by…

Q: 8 1. Convert complex nos. into standard form (→ √3 – i)ª

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Q: (a) Consider a rectangular hyperbola H and a circle C intersecting H at four points P, Q, R and S.…

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Q: find the integral of the function fix, 41= (x²+y²)³ the region between the two circles of GV RV…

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Q: A formula of order 4 for approximating the first derivative of a function f gives: f(0) 1.0982 for h…

A: Solution:- option (2) is correct

Q: Define a relation on N by (a,b) ER if and only if E N. Which of the following properties does R…

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Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with -0.1, find the relative error…

A: We can solve this using runge kutta method and relative error

Q: ketch the surface

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Q: Show that every 2 x 2 matrix A of determinant 1 is the product of three elementary matrices. This…

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Q: The advertising company creates histograms, shown in Figure 1, for the podcasts data, but forgets to…

A: 1) This is a Discrete Data because Number of Audiences is some particular Number which will take…

Q: 12 Two towers AB and PQ stand on level ground. The angles of elevation of the top of the taller…

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Q: A B An airplane used to drop water on brushfires is flying horizontally in a straight line at 180…

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Q: f(x) = x²+1, if x < 2 7-x, if x ≥ 2

A: Given: f(x)=x2+1,if x&lt;27-x,if x≥2 To find: Critical numbers of given function.

Q: Consider xy' = y(lnx-lny) with y(1) = 4. Using Runge-Kutta method with h-0.1, approximate y '(1.3).…

A: option c is correct i.e. (c) -1.92711

Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with h=0.1, approximate y'(0.2). (a)…

A: Given y′=2y+3e2x,   y(0)=2,   h=0.1Forth order R-K methodk1=h f(x0,y0) = (0.1) f(0,2) = (0.1)⋅(7) =…

Q: 3.a) Apply the Trapezoid and corrected trapezoid rule, with h = 1, to approximate the integral…

A: Given: f(x)=ln1+x2, a=0, b=1 and h=18 To find: (a) The integral ∫01ln(1+x2) dx. (b) The minimum…

Q: 3. Consider the vector field F(x, y) = (2xy, x² - sin y). Evaluate F.ds π where is the curve c(t) =…

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Q: -a+b+c b The linear transformation L: R4 → R³ is given as L (0)-[] b с 2a-b a. Determine the matrix…

A: (a) If Tx=Ax, then A is called matrix of linear transformation. (b) λ is called eigen value of a…

Q: Suppose y(3)=5 is the initial condition of a differential equation. Using Euler or Runge - Kutta…

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Q: 1. The curve shown below can be expressed both as a function of x, y = f(x), and as a function of y,…

A: As per our policy, we are allowed to attempt only first question remaining post separately.Q(1).Let…

Q: 2. Find the general solution of cos² x sin x dy + (y cos³x - 1) dx = 0

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Q: Solve in terms of t, u"""" + u"""' = 0.

A: Given the differential equation is u"""" + u"""' = 0.  Here the auxiliary equation is r8  + r7 = 0.

Q: 12 Two towers AB and PQ stand on level ground. The angles of elevation of the top of the taller…

A: (A) ∆BPQ∠BPQ  + ∠PBQ + ∠PQB =180°∠BPQ + 20°+90° =180°∠BPQ = 70°In ∆APK∠PAK+∠PKA+∠APK = 180°∠APK  =…

Q: 7. Find the exact x-value where the function f(x) = x + ln (x² - 1) attains a maximum value. An…

A: Solution:-

Q: By using Laplace transform to solve y" + y = e with y (0) y (0) = y" (0) = 0, what would be Laplace…

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Q: Solve the differential equation using 3rd order RK method dy/dx = yx3 – 1.5y, y(0) = 1 find y when…

A: The solution of given differential equation using third order rk method.

Q: 4. (i) Let f(x) = x² + 3x³ + 2x² +2 and g(x) = x² + 2x + 1 € Q[x]. Find the unique polynomials q(x),…

A: Given: f(x)=x4+3x3+2x2+2 and g(x)=x2+2x+1 To find: (i) Unique polynomials q(x), r(x)∈ℚx such that…

Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with h=0.1, find the relative error…

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Q: 4. Evaluate √3x²e¹² da + 2x¹yev dy where the open curve C is the semicircle x² + y² = 5, y ≥ 0 going…

A: 4. The given integral is ∫C 3x2ey2dx +2x3yey2dy where C is the semicircle x2+y2=5, y≥0 To find: the…

Q: Suppose f"(x) = N₂(h) + a₂h³ + a₂h¹ + a₂h³ +.. When calculating N, (h) using Richardson…

A: Solution

Q: Exercise (1-3): By Charpit method solve the following PDE (1): p²x+q'y=2

A: Since you have posted a multiple questions. So,  we will solve only first question  for you. To get…

Q: Examine the continuity of f(z) = 2-√z+4 Z at z = 0

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Q: Determine (without solving the problem) an interval in which the solution of the given initial value…

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Q: ܒܢ J nπL s²L²+ n²π²] 22

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Q: 3.a) Apply the Trapezoid and corrected trapezoid rule, with h =, to approximate the integral…

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Q: Suppose f(x, y, z)=+P-(1.2.3). A. Find the gradient of f V/= 1+ J+ Note: Your answers should be…

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Q: y = = [ot (x): [=-x≤x≤r]

A: Given function is y=−cotx. We have to plot the graph of the given function in −π≤x≤π.

Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with h=0.1, the k4 needed in the…

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Q: Let Q = R\Q be the set of irrational numbers in R. Consider A = Qºn (√2, √3) as a subset of R,…

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Q: If a, ß be the roots of ax² + 2bx + c = 0 and a +8, ß+8 be those of Ax² + 2Bx + C = 0, then 2 6² b -…

A: We have to find the required value

Q: 5. Use Linear Approximation to estimate e(-0.01). Provide your answer in 2 decimal places. Do not…

A: We have to find the estimate value of  e-(0.01) Using linear Approximation.

Q: Consider xy' = y(lnx −lny) with y(1) = 4 . Using Runge-Kutta method with h=0.1, the k3 in the…

A: The given O.D.E is xy'=ylnx-lny with y1=4. To find: The value of lnBA

Q: A study examined the relationship between a nurse's assessment of a patient's facial expression and…

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