A boomerang is thrown such that its position at any time t> 0 is given by the function r(t) = - 4t2 - 3. Determine the time that the boomerang turns around (changes direction) a) O-3 b) O c) O d) 04 e) 02

Q: State the signs of f"(x) and f"(x) on the interval (0, 2). (0, 6) (7.2343146)

A: To determine the sign of 1st and 2nd derivative on the interval (0, 2).

Q: Q4) ut A = :) al let fox)- 2x_4x+5 and g(x)= x?42x + 11, Fiind + 2X + 11, Find @ A ; DA ; © PCA);…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

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Q: Write a in the form a = arT + aN N at t-0 for R(t) = t?i + (t +); + (t - }c")k

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Q: Evaluate F. dr along the line segment C from P to Q. F = -8xi+y j; P(-2,0), Q(7,0) F• dr =

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Q: True or False. 0 <t< 8 f(t) = } Ut – 8| t2 8 is equivalent to g(t) = -u3(t) + u3 (t)|t – 8||

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Q: sove for m in terms of r and T. [(1-m)(1+r)]T=1/2

A: The answer is given as follows.

Q: The domain of the function g(t) = vt – 2 is O R-{2} O [2, 00) O R о (-о, — 2) n (? m)

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Q: D Express the interval in (a-k, a+R) aad 1 x.-alc.R I(3x+1)?(<!

A: |(3x+1)2| &lt;1 both side we take square roots |3x+1|&lt; +1 3x+1 &lt;+1 3x+1&lt;1    or    3x+1&lt;…

Q: 5. Show that T = + y? satisfies the equation T + Tyy = T³

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Q: Evaluate the convolution, f(t) * g(t) = 8t*e', then evaluate at t = 2.

A: If f and g be two functions that are piecewise continuous on every finite closed interval 0≤t≤b and…

Q: dA Find the general form of the function that satisfies = - 7A. dt A(t) =| %3D

A: Given query is to find the general solution of the differential equation.

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A: Find the derivative of function at x =0

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A: Solution:

Q: z) = 8x? In (5y + 9z). Find the range of tl %3D

A: We have to choose the correct option according to the given option

Q: Find the convolution f (t ) *g(t) f(t)= g(t)=sint

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Q: Let f(x) = V42 – r and g(x) = 2? – a. Then the domain of f ogis equal to [a, b] for T. a and b =

A: fog= (42-(x2-x))0.5       = (42-x2+x)0.5

Q: Suppose that SpaceX launches a rocket at seconds and that its height, in meters above sea-level, is…

A: Given: Suppose that SpaceX launches a rocket at t=0 seconds and that its height, in meters above…

Q: Using the coffee demand function, Q = 8.56 − p − 0.3ps + 0.1Y, show that sugar is a complement for…

A: Given data: The expression for the coffee demand function is Q=8.56-p-0.3ps+0.1Y. Differentiate the…

Q: (d) Show that the function T : R² →R² defined by T(Vi,v2) = (Vi – 2, vì + 2v2)

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Q: hup lict funcrion F(xig) = x?y -eto =0 P(e, 1) Find y" (e) = ?

A: Here to use implicit diffrentiation method for solving the problem

Q: F.ds, W by the pl

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Q: Given a function f(x,y,z) = 6x² In (8y + 9z). Find the range of the function. O z > -0.89y o [1,…

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Q: Let f be a function such that f(u) du 10. What must be the 1 value of x ) dx? 2

A: Use substitution method

Q: Find the linear approximation at x=0 to 1/(sqrt(2-x). Write your answer in the form y=Ax+B.

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Q: Write a in the form a = a-T + an N at t-0 for R(t) = t²i+

A: Given Rt¯=t2i+t+13t2j+t−13t2k We have to write a in the form a=aTT+aNN Since, Rt¯=t2,t+13t2,t−13t2…

Q: The function, r= 3t°, y =ť –t is concave upward on the interval (a) (-∞,0) (b) (0, 0) (c) (-0,0) (d)…

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Q: Show that the function f(x, y) = (y + ax)²ev+a satisfies the equation given by %3D a2

A: Please see the explanation below....

Q: What is the tangent of 0? 6 D 6V11 11

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Q: Consider the function h : Nx N → Z given by h(n, m) = 2n² . m. What is the image of h? Prove your…

A: Introduction: A function has a domain and a range. The domain is the set of all input values of the…

Q: Given f'(u) = e^−u − 6u^2, find f(2) − f(−1).

A: Given

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Q: show that T = 1/sqrt(x2 + y2) satisfies the equation Txx + Tyy = T 3.

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Q: sketch the interval (a, b) on the x-axis with the point c inside. Then find a value of d &gt; 0 such…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find whether the function F= 5yz? i+(3x– 2)}+(x² – xyJk is solenoidal.

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Q: Use a formula to express w as a function of t if w = s2 + 1 and s = t − 8.   W=

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Q: Je b. Find of f(x,y) = ye*"? ax' ay %3D

A: Use logarithmic differentiation to solve it.

Q: Evaluate F· dī where C F = = , and C is given by - T(t) = , 0 < t < T 0 <t<

A: Given

Q: Describe the long run behavior of f(x) AS I→ ∞, f(x) → ? v As → ∞o, f(x) → ? ✓ || H 2³

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Q: Use a formula to express w as a function of t if w = s2 + 1 and s = t − 2. w =

A: Explanation of the answer is as follows

Q: Use the figures to evaluate the function if f(x) = sin x. (X, 1) | x² + y² = 1 f (α+ β) x2 + y? = 4…

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Q: Use a formula to express w as a function of t if w = s2 + 1 and s = t − 8.

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Q: What is the degree of f (x, y) = 2y + Væ² + y? ? O 1 O 2 O 1/2

A: We can solve as follows

Q: If F = 3x?i + 5xy²j+ xyz³k, find (V x F) at the point (3,1,2).

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Q: c = , d.f. = __te =_ E = , interval: to

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Q: B E F A D

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Q: sy,z) = 8x? In (5y + 9z). Find the range %3D

A: We have to choose the correct answer from the given option according to the given option

Q: Write a in the form a = arT + an N at t-0 for R(t) = t2i +

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Q: The formula for the midpoint of (x1, y1) and (x2, Y2) is: M =| O True O False

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.