Q4) Find for the following functions (- dx Зх +4 %3D 2x+3 6. y = tan-1 V4x3 - 3 %3D

Q: Q10. For the function f(x, y) = x³e³y_find the maximum value of its directional derivative at the…

A: Here, f(x,y)=x3e3y⇒∇f=∂f∂x,∂f∂y=3x2e3y,3x3e3y⇒∇f(1,0)=3(1)e0,3(1)e0=(3,3)

Q: D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

A: Given that     D(x) = -3x/10 + 8     S(x) = x/5 + 3

Q: 8. Given 8. dx = 16 and f(x) C g(x) dx = -5, evaluate the following. %3D (a) [F(x) + g(x)] dx (b)…

A: Given query is to find the value of the integrals.

Q: Use Newton's method to approximate a root of the equation x + x + 4 = 0 as follows. Let 1 = - 1 be…

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Q: The Inverse Laplace Transform for 5/3S - 2/ ((3(s+3)) is

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 +1 1 lim t→+∞ \ 3t2 +4’ 6t (?, ?)

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Q: 1. Find the particular solution using the Initial condition. xy'-y x.y(1) 7. Finally, sketch a slope…

A: Follow the procedure given below.

Q: Differentiate the function. g(u) = 7u + V 5u

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Q: Find the average value gave of the function g on the given interval. g(x) = 3x, [8, 64] gave =…

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Q: DEFINITION 7.1.1 Laplace Transform Let f be a function defined for tN 0. Then the integral L{f{t)}…

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Q: 2 sin (csc 2x) dx

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Q: The discontinuities of the function f(x) = %3D 4х-9 are: х2—2х-15 Select one: O 5,3 O -5, -3 -5,3 O…

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Q: is said to be the Laplace transform of f, provided that the integral converges. to find L{f(t)}.…

A: Let's find.

Q: Dx) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and…

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Q: Use Newton's method to approximate a root of the equation +x + 4 =0 as follows. Let 1 = - 1 be the…

A: The given equation,    x3+x+4=0

Q: Given f''(x) = 4x – 6 and f'( – 1) = – 2 and f( – 1) = 4. Find f'(x) = and find f(2)

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Q: 4- Find lim,: ( -) 10 20 (You cannot use numerical table method). tan(2)-1 tan?(2)–1)

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Q: Evaluate the limit sin 9x lim I0 sin 3x

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Q: An automobile traveling at the rate of 20 m/s is approaching an intersection. When the automobile is…

A: This question an be solved using the concept of rate of change of physical quantities.

Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). 3 r(t) = e"i+ etj %3D K(t) = ||

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Q: f(x,y) = 2y3–3y² – 12y+2x2 – 4x+2.

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Q: A Triangular number counts the objects that form an equilateral triangle. The nth triangular number…

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Q: Estimate cos(π/4 - 0.1) + cosπ/4

A: Solving

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t2…

A: As per given  We have to solve above question  Given  V(t)=t2-2t-8

Q: X – 1 limx → 1 V 4x – 2/x -

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Q: 7- Use the limit definition to compute f' (x) and find equation of the tangent line at r = 3. f (z)…

A: topic - derivative of a function using limits

Q: Question 3 Find the area enclosed by the curves y y = 2 V1- 9x2 O V5- 9. 2n B 3 5n D 6

A: Solution is given below:

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x-0 sin 2x x2-16 2. lim X4 (Vx+5)-3

A: Using l hospital rule.

Q: 1-

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Q: - Ose the tranfiorms from the "Table of Lapiace Transformso fnd the Lpce of the function below. You…

A: Given problem:- Find the laplace transformation of f(t) =(1+t)3

Q: If f(x) = 4x(sin I + cos I), find f'(r) -| 4x cos(r)- 4z sin(r) +4 sin(r) +4 cos(r) f'(1) =

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Q: dy Find dx 4t t dt + 2 y = dt - t° + 2 - 3 6. dy dx (Simplify your answer.)

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Q: the integral dx Va? – x? e may use x- educe the integral to a sine and dx= a cose de substitutions…

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Q: Evaluate the limit tan x lim z0 2x

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Q: The acceleration function (in m/s²) and the initial velocity v(0) are given for a particle moving…

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Q: 34 10- Find equation of tangent line at the point (0, T) for Cos (7x- y) %3D 4y

A: Solved below

Q: Evaluate the indefinite integral. x2 dx V0.2x3 + 2.7 + C

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Q: Find the profit function for the given marginal profit and initial condition. Marginal Profit…

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Q: 4 dx 16 + x² 2 dx X/x² – 4 2

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Q: Evaluate the integral. 3 if -2 < x< 0 f(x) dx where f(x) | 4 – x² if 0 <x< 3

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Q: In Exercises 1-3, find the general solution of the differential equation specified. dy 3. 2t 1+ 124…

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Q: A ball is shot from the ground straight up into the air with initial velocity of 49 ft/sec. Assuming…

A: Let's find.

Q: Determine equation of the line in vector form, parametric form, symmetric form and scalar equation…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 10 Consider the function f(x) Let F(r) be the antiderivative of f(z) with F(1) - 0. Then F(z)

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Q: I. Find the antiderivatives of the following functions using the substitution rule. Write your…

A: According to our guidelines we can answer only one question or 3 subparts of a question, other…

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 4t2 – 2 sin(5t)…

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Q: 7 5 5. sec '(In t) tan° (In t) dt t

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Q: 13. Find the mass of a thin funnel in the shape of a cone z = x² + y²,1<z< 4, if its density…

A: It is given that, the equation of a cone is z=x2+y2,1≤z≤4 and the density function is δx,y,z=10-z.…

Q: Evaluate the definite integral. e141 i + e-j +t k )dt O e 4 – 1 i + (e-1 – 1) j +, k - 14 (e4 – 1) i…

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Q: Describe the graph of the equation. (8 – 21) i + 13rj r = O It is a plane in 2-space through the…

A: I have appended the formula used in the solution part.