Find the limit. lim (t i – 4 j + t k) lim (t i – 4 j+? k) i i+ i j+ i k

Q: Use Stokes' Theorem to evaluate F. dr. z = 4 – 22 – y? F(x, y, z) = 2zi + 10xj+ 3yk where C is the…

A:

Q: Evaluate the definite integral. i+ej+tk)dt O es - 1 -- (-~" - 1) + 5 O es i- e- 5 O es i + (e- - 1)…

A:

Q: Consider the diagram above, and select each statement below that is true. [n n¹] is a 1D projection…

A: The first option is correct.

Q: he conclusion of Green's Theorem by evaluating both sides of each of the two forms of Green's…

A:

Q: Find the k-component of (curl F) for the following vector field on the plane F=(x+y)i + (8xy)j

A: Solution: F=(x+y)i + (8xy)j       P             Q k-component

Q: Q8/ A tank contains 100 gal of fresh water. A solution containing 1 lb/gal of soluble lawn…

A:

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. dy

A:

Q: Write the integral in terms of u and du. Then evaluate. u = 812 + 1 (Use symbolic notation and…

A:

Q: 11. If f"(x)=-4sin 2x, f(0)=0and f'(0) =2, find the value of f 4

A:

Q: 10. Find the position function s(t) given acceleration a(t)= 2t if v(2) = 0 and s(2)=1.

A:

Q: The population of a city is 75,000. If the population is declining continuously by 3.7% per year, in…

A:

Q: A 25-year-old woman burns 550t cal/hr while walking on her treadmill. How many calories are burned…

A: A 25 year old woman burns 550t cal/hr while walking on tradmill.

Q: 4. The volume V of a sphere is directly proportional to the cube of the radius. With k as the…

A: Option D is correct

Q: L(25 — х?)3/2. |dx

A:

Q: Let f(x)= = z+1 x³2x² + x

A:

Q: Evaluate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

A:

Q: The position of an object attached to a spring is given by s (t) = cos(4t) — —sin(4t), - where t is…

A: The position of an object,st=14cos4t-16sin4t on the interval 0<t<3

Q: Verify Green's Theorem by evaluating both integrals y² dx + x² dy = / dA дх ду for the given path.…

A: Here we have to verify the Green's theorem.

Q: P has degree 3 and zeros 3 and i. P(x) = | I

A: Given query is to find the polynomial.

Q: Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and…

A:

Q: Find the slope of the tangent line to the curve 4x² 3xy - 2y³ = - 26 - at the point (4, 3).

A:

Q: 4. A graph of a function y = f(t) is shown below. Use this graph to answer the following questions…

A: We will use If f(x) is a function. Then roots of f'(x) is called critical points and if f'(a)=0.…

Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A:

Q: QUESTION 12 Find d²y/dx². x=1+1²y=t-³

A: Given;  x=1+t2, y=t-t3

Q: Full Solutions 1. CHOOSE ANY TWO of the following problems and determine i) the Optimization…

A: Note: There are multiple questions. No specific question has been asked.So, We will solve the first…

Q: Calculate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

A: Given; I=∫4xsin4xdx   ....1   As we know that; ddxax=axlna∫sinxdx=-cosx+C And ∫a·fxdx=a·∫fxdx, where…

Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

A:

Q: |(sec (x)) dx

A:

Q: Use Green's Theorem to evaluate the integral (3x² – y)dx + 3xdy where C is the circle a? + y? = 1…

A: As we know from the Green's theorem; ∫CMdx+Ndy=∫∫D∂N∂x-∂M∂ydA   Given; I=∫C3x2-ydx+3xdy So, M=3x2-y…

Q: The total cost (in dollars) of producing a golf clubs per day is given by the formula C(x) = 450 +…

A:

Q: Write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 9x²,…

A: Given query is to find the equation of the parabola.

Q: 10. Using the graph below of the function f(x), identify the approximate interval(s) where the first…

A: Given that,

Q: Let F(x) = f(x³) and G(x) = (f(x))*. You also know that a = 7, f(a) = 3, f'(a) = 6, f'(a³) = 7 Then…

A: To find, F'(a) and G'(a)

Q: A particle moves in a straight line with the given velocity v(t) = 24 – 6t (in m/s). Find the…

A:

Q: y? = x and y2 = 2 – x %3D

A:

Q: Determine the following general antiderivatives. [3x (x²-5)³4x [Axe+²7 tan(+²7) dx 10 d. cos(x)…

A:

Q: Given Cost and Price (demand) functions C(q) = 100q+40000 and p(q) = -2.4q+950, what is the marginal…

A:

Q: tan(5. x) dy dx Y = Find dy da = Type sin(x) for sin(x), cos(x) for cos(x), and so on. Use x^2 to…

A:

Q: If a person learns y items in æ hours, as given by y = 19V2?, find the rate of learning for a person…

A: We need to find the rate of learning.

Q: 8. Find the derivative of the function f(x) = x ² - 10x + 3 using First Principles.

A:

Q: 24 ue'sin(s + 2t)

A:

Q: A bottle of milk initially has a temperature of 79°F. It is left to cool in a refrigerator that has…

A:

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

A: topic - application of derivatives and integrals

Q: 6. Find the intervals on [0,27) where f(0) = sin² (0) is concave upward/ concave downward.

A:

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

A:

Q: Compute the Jacobian for the change of variables given by u= x+y and v=x-y. O a.-2 O b. 1 2 O c. 1 2…

A:

Q: Find the average value of f(x)= e^-x on the interval [0,2]

A:

Q: Find the area under the given curve. y = Vx +6, from x = 0 to x = 16 The area is (Simplify your…

A:

Q: The gradient of f(x, y, z) = xy²z³ at the point (1, 2, 1) is

A:

Q: -8 27 -6 -5 -4 -3 -2 ਆਰਡਰ 41 3 1 -2 -3 The curve above is the graph of a sinusoidal function. It…

A: Given query is to find the graph of the function.