Note Answer One Question Q1 The following data is provided for the velocity of an object as a function of time: 10 15 20 25 30 35 40 V. m/s 19 32 46 51 47 63 66 75 Limiting yourself to trapezoidal rule and Simpson's 13 rule, make the best estimate of how far the object travels from t= 0 to 40 s?

Q: Q2) Solve the D.E xdy + (2y – x* + 3x)dx = 0 %3D

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A: Answer and explanation is given below...

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A: Answer is in below steps.

Q: 1 Find f'(-1) if Ax) = (2x + 1)², O-4 04 O-1

A: The given function,       fx=12x+12

Q: Q3) Evaluate triple integral , * dz dx dy.

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Q: Integral using trigonometric sub The answer in the integral is: sin(20) + C 8 4 If x= 2sece then x/2…

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Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: Solve the following

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Q: /2n?

A: The given series is: ∑n=1∞(-1)n(-1)n2n2+5=∑n=1∞(-1)2nn2+5n2=∑n=1∞1n2+5n2

Q: Consider the following function and dosed interval. fx) = x2/3 - 1, [-27, 27] Is f continuous on the…

A: F(x) is not differentiable on (-27, 27)

Q: A. LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS 6. (D5 – 16D³)y = 0 7. (D² – 2D + 5)y = 0

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Q: Find each of the following indefinite integrals.  c. Z (r+2)^2/r^3 dr

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4-x from above inside x = y2 ,x = 4.

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Q: V. Let f(x) be a differentiable function such that for all æ > 1, • f(x) > 1, • f'(x) < f(x) and lim…

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Q: A line with positive slope passing through (-1, 1) and intersects the parabola y = x² at the point P…

A: We have to find co-ordinate of P

Q: 4. Find the Laurent series of the following function : f (z) = (z + 1)(z + 3) 1 region 2 < |z – 1| <…

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Q: Question Using Rolle's theorem for the following function, find all values c in the given interval…

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Q: H.w Pind the ro.t when [!,3} by Disection?

A: We have to find the root using Bisection method.

Q: He we 2# is Hhe difference what continuty and uni formaly シー continuty.

A: A function f:A→Rf:A→R is continuous at a point c∈Ac∈A if, for all ϵ&gt;0ϵ&gt;0, there exists a…

Q: 1 Calculate the difference quotient for f(x) = at a = 4. V2x + 7 (Express numbers in exact form. Use…

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Q: n Vy(x- y) + y² + 6

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Q: (-1)" V2n² + 5 Given: power series > (x+ 1)" n=1 i. Determine if the resulting series of constant…

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Q: Let f(x) be a differentiable function such that for all x > 1, f(x) > 1 f(x) and f(x) < lim f(x) = 1…

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Q: Let a = ci + jand b = 16i + 12j. Find c so that the angle between a and b is Round your answers to…

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Q: 8. Find the derivative of (logsx?). dx 2 A. x In 5 1 В. x In 2 С. x In 5 D. 2x In 5

A: Solving the problem by finding the value of the derivative. For the question no 8. Option A is…

Q: Calculate two iterations of Newton's Method for the function using the given initial guess. (Round…

A: Explanation of the answer is as follows

Q: a ) Σ-1 (-1)"-1 Zn=1 2n+1

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Q: Evaluate the following limit: x² + x- 2 lim- x-1x2- 2x + 1 If it does not exist enter DNE. Round to…

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Q: Given the set of parametric equations x = 2t2- 1 and y = 3t + 4, eliminate the parameter t and…

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Q: ) Oppositely directed to v = (15, –18) and half the length of v. w = (?, ?)

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Q: 2. S dx I+,x

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Q: The limit represents a derivative f'(a). Find f and a. V3 sin (5 + h) lim 2 h→0 h (Express numbers…

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Q: (-1)" Given: power series (x + 1)" 2n2 + 5 i. Determine if the resulting series of constant terms…

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Q: el-vidx

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Q: Solve the particular solution of the equation dy/dx = 3x² - 2x, when y=2 and x=-1.

A: We can solve the given problem as follows:

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Q: Use the appropriate Product Rule to evaluate the derivative, where ri(t) = (9t, -10, -t°),r2(t) =…

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Q: The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

A: Let r be the radius of spherical ballon

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Q: Determine if the improper integral (1 e" )2 dx converges or diverges. If it converges, find its…

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Q: Find f"(3) if Ax) = X-2.

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Q: +oo (2x – 1)" V4n + 1 Consider the power series n=0 a. Show that the series is conditionally…

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Q: The limit represents a derivative f' (a). Determine f(x) and a. 14h lim 1 h→0 (Express numbers in…

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Q: EXAMPLE 3.1.1 Find the equation of the tangent line to the graph of f() = x² at z = 2 . Solution m =…

A: We have to find the equation of tangent.

Q: -ions of the line through (-1, –2, 5)

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Q: You are stationary on the ground and are watching a bird fly horizontally towards you at a rate of 5…

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Q: Find f"(-1) if Ax) = (x² -x+1)(x +1). O -1 3. O -3 9.

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