Let 7 (t) = < 5t? + 5, tª + 3t, In a. Determine the coordinates of the point on the curve traced out by r(t) when t = 3. 50 90 b. Find a direction vector for the line tangent to the graph of r at the point where t = 3 30 c. Find a parametric equation of the line tangent to T(t) at t =3 r(t) = 50 + 30t y(t) = z(t) =

Q: b) Find the inflection points. 4. For the given function find the local extrema using the Second…

A:

Q: d d Calculate ri(t) · r2(t)] and r:(t) x r2(t)] first by differentiating dt dt the product directly…

A:

Q: 8. If V represents the volume of an object, what does AP represent? - dt

A: dydx-Represent the Rate of change of 'y' with respect to 'x'. Here, 'y' is dependent variable and…

Q: 1 Let F be a vector field in IR whose components have continuous partial derivatives. Consider the…

A:

Q: Solve the following differential equation (6х' — у +3)dx + (Зу* — х- 2)dy

A: Here, i am providing the handwritten solution

Q: A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10…

A: In the given question first, we will form a figure using the given information   And we will use the…

Q: Find the surface area of a sphere at the instant when the rate of increase of the volume of the…

A:

Q: Solve the following differential equations of (x' +y')dx + (2xy + cos y)dy

A:

Q: Sheldon is being chased back-and-forth by a dog along Euclid Avenue. His directed distance (in…

A:

Q: Use the Comparison Test to determine whether the series is convergent or divergent. 00 ,7/8 n' n = 2…

A: The given series,    ∑n=2∞1n78-1

Q: If f(x) = V4x + 1 find f"(2). O 4/27 O 213 None of these O 2/3

A: Topic:- Derivatives

Q: Given the formula B V R, where statement B is true and statement R is False, the whole formula would…

A:

Q: (a) Prove that the series Vn + 2x - Vn +x Σ n=

A: answer is in next step

Q: How would you evaluate |F-dr, where C is the curve with param etrizati on r(t) for astsb?

A:

Q: Match the vector field with its graph. F(x, y) = yi 6. -6+ y 十H HH

A: We need to match vector field with its graph.

Q: ||r(t) × r"(t)|| ||r"(t)||* Use the formula k(t) = to find k(t). r(t) = e"i+etj K(t)

A: We have to find k(t)=?

Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use dx x(In(x?))5

A:

Q: Comparing Graphs of Derivative Functions Date Given the graph of f(x), sketch an approximate graph…

A: Given graph of function f(x)

Q: summation

A:

Q: Evaluate using Integration by Parts. (Use symbolic notation and fractions where needed.) хебх+4…

A:

Q: Sketch the graph of the function f(x) = x³ – 2x² – 5x + 6 using calculus – based analysis. -

A: Given problem:- Sketch the graph of the function f(x) = x3 – 2x2 − 5x + - 6 using calculus - based…

Q: Let C be the curve represented by the equations x = 5t, y = t", (0 < t < 1). In each part, evaluate…

A:

Q: 7- Differentiate K(x)=(Vx)(5x²+1)³

A:

Q: sinex) sintpx) x

A:

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: Use limit concept

Q: Suppose parametric equations for the line segment between (-2, 8) and (7,3) have the form: a + bt…

A: This question can be solved by substituting the values of x,y and t in the given equations.

Q: Evaluate the integral. 3-/4 5 sec e tan e de

A:

Q: you save 270 PER QUARTER for retirement in an account that earns 8% interest per year compounded…

A: Given query is to find the amount accumulated.

Q: A particle is moving with acceleration a(t) = 18t + 4. its position at timet = 0 is s(0) = 6 and its…

A: Solution of given question is written in below steps.

Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation…

A:

Q: uilding that is 225 feet tall casts a shadow of various lengths as the day goes by. An angle of…

A:

Q: Find the area oF the regioN eNclosed between the curves de Fived by the equations y =Vx +2, y: x,…

A:

Q: Use the price-demand equation below to determine whether demand is elastic, is inelastic, or x=f(p)…

A: Here I am providing my handwritten solution.

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

A:

Q: Find the area of the shaded region. y=x-4 y= /2x 2. 8. 10 x -4 2.

A: Given query is to find the area of tha shaded region.

Q: Find a particular solution to the DE: y"+ 3y' – 4y = e* xe B. Yp = C. Yp = x²e* D. y, = xe-x E. None…

A:

Q: 55. At 9 A.M., ship B is 65 miles due east of another ship A. Ship B is then sailing due west at 10…

A:

Q: Ben is a fisherman with a boat in Rhyl harbour. This is part of a graph of the depth of water at the…

A:

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: We use the concept of derivatives to find the absolute minimum and absolute Maxima

Q: Suppose that z = f(a, y) is differentiable at the point (1024, 1024) with, (1024, 1024) = 5…

A:

Q: Determine the range of f(x,y)=tan 2+x +y

A: Here the value of x2+x2+y3 can vary from -∞ to ∞. The possible values of tan-1x2+x2+y3 is…

Q: Given g(x) =- 1 g(x)-g(a) find -, where x# a. %3D x+3 X-a

A: Solving the problem by finding the value if given expression.

Q: Find the slope of the tangent line to the polar curve r = cos(30) at 0 = 7. Enter as an integer or…

A:

Q: 5. You are not allowed to use the graphing calculator For the given equation f(x) = x³ – 6x2 +9x- 2…

A: Only 5 solved... According to given   F(x)=x3-6x2+9x-2

Q: B. Find the value of (r+1)dx in the following three ways: a. Using elementary geometry, interpreting…

A: answer is in next step

Q: Answer each question appropriately. f(x) dx = 9. Find -2 f(x) dx , if f is odd. Suppose that

A:

Q: -2000x has the marginal-demand function D'x)= where Dx) is the number of units sold at x dollars per…

A: First we'll integrate and the we'll put the given value. So i am providing my handwritten notes…

Q: Given the formula B V R, where statement B is true and statement R is False, the whole formula would…

A: We have to choose correct option

Q: Let 7(t) = Find )dt (don't include the +C)

A:

Q: 3 Find the slope of the tangent to the graph of f(x) = /x+5 at the point where x= 4.

A: