Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (7t + 3)i + tj, 0 sts1

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

A:

Q: Describe the graph of the equation. r = 2 sin 10t i + 2 cos 10t j O It is a circle of radius 10 in…

A:

Q: S sin x In(cos x) dx X

A:

Q: y = x°y=/2;y(1) = 1 -1/2; y(1) = 1

A:

Q: Peaive marima and, minima, 4 any tar the funchno If there is not an answers write N/A Wde ms wefs as…

A:

Q: Calculate the area enclosed by the curve f(x) = x³ – 6x2 + 8x and the x-axis.

A: Given query is to find the area enclosed by the curve and x Axis.

Q: sheet of paper for a poster is to be 18 ft2 in area. The margins at the top and bottom are to be 9…

A: Ler the the dimensions of the sheet is  x and y in order to maximize the print area

Q: Suppose that Po is invested in a savings account in which interest is compounded continuously at 6…

A:

Q: At which point will the plane 2x + 4y – 3z = -48 and the line given by the parametric equations x =…

A:

Q: Given the function below f(x) = V-80x + 144 Find the equation of the tangent line to the graph of…

A: Given :

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A:

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A: Explained below

Q: Find V. (V x F), if F(x, y, z) = 6e"²i+ 2xe³j – 3ek. - V·(V × F) =

A:

Q: x2 - 6x + 8 lim X 2 X - 2 1

A: The objective of the question is evaluate the limit.

Q: Use the formula K(t) = r(t) × r"(t)|| ||r(t)||* to find k(t). r(t) = 11 cos(t)i+11 sin(t)j + 6tk…

A:

Q: Evaluate the following limits. If needed, enter INF for oo and MINF for -oo. (a) lim (Va + 3r +1-1)=…

A:

Q: Determine the gradient of f(r, y) = ez sin(5y) at (r, y) = (3, – 1). Round to 2 decimal places. V…

A: Given query is to find the gradient at indicated point.

Q: Suppose that f(z, y) = z² – zy + y² – 5z + 5y with z² + y² < 25. 1. Absolute minimum of f(x, y) is…

A: Solve the following

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

A:

Q: y6 16 (1). Consider z as a function of the variables x, y which is defined by z = ln(x®y) + and let…

A:

Q: Find curl (4z i+ 5x j+ 8y k). curl(4z i+ 5x j+ 8y k) = ( )i +( i j+( i )k

A: To Find : curl(4z i + 5x j +8y k)   Note that : If F=〈P,Q,R〉 is a vector field in ℝ3, and Px,Qy, and…

Q: 3. If dt , find g'(2). 5. g(x) =

A:

Q: A stone is thrown vertically upwards, from the edge of a 5 m tall cliff with an initial velocity of…

A:

Q: Kuya Bill is selling 'Bill phones'. If the cost for selling r phones is given by 10000 C(r) = 120x +…

A: Given, Cost function, C(x) = 120x + 10000/x - 2000 Price Dand function, p(x) = 1000 - 2000/x2 + 200x

Q: f(x) = 2 – 5x², - 5< x < 1.

A:

Q: Suppose that in a memory experiment the rate of memorizing is given by M'(t) = – 0.004t? + 0.4t,…

A: Given,  M'(t)=-0.004t2+0.4t

Q: x+2 Solve: x-1-3 <0

A:

Q: If a rock is dropped from a height of 193 ft, its poistiont seconds after it is dropped until it…

A:

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

A:

Q: A man has $380,000 invested in three rental properties. One property earns 7.5% per year on the…

A: Given problem:- A man has $380,000 invested in three rental properties. One property earns 7.5% per…

Q: A particle's position at time tis given by r(t)= (3t",4t+1,-t). Find a, att=3.

A:

Q: Let floo) = 0e 5 and gloo) = 2a19 Detemine Cgof) (x) 2079. %3D %3D

A: Topic:- function

Q: 5x? + 8x + 3. If Aæ 0.3 at x = 5, use linear approximation to estimate Ay Let y Ay =

A:

Q: ||r(t) x r"(t)|| Use the formula k(t) = to find k(t). ||r"(t)||° r(t) = t'i+ t°j K(t) =L

A:

Q: Given the function g(x) = 8x³ + 12x² – 48x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

A:

Q: Let h(x)= f(g(x)) where f(x)=tanx. Then h'(x)= a) f'(tan x) g'(x) b) g'(x)tan(g(x)) c) g(x)…

A:

Q: Find a plane through the points (4,-3,-4), (-6,2,8), (3,-8,8)

A:

Q: 7. When a vehicle is said to be travelling at -35 km/h, what does this infer?

A: We can explain the answer in the following steps.

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: 2.x4 + x3 x4 xp-

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

Q: /1 5/2 Find the length of the curve r (t) = ( t,4t,25t ) for 0<t <1.

A: Use the parameterization of curve for finding the length of curve .

Q: (b). lim zInz² et

A: To evaluate: limx→0 xlnx2ex Using logarithmic property we can write the given limit as  limx→0…

Q: Qu= O.4 log (E+0.44 435 %3D Qa - 0.249(log Ea)-O.I77 Q8= 0.227 (log E3)-0.839 Q3= rearange equations…

A:

Q: Suppose a curve is traced by the parametric equations 3(sin(t) + cos(t)) = x у 3 18 — 6 соs"(€) — 12…

A:

Q: Save & Exit Certify Lesson: 6.4 Area (with Applications) DSHUN EDWARDS 4/9 Question 6 of 9, Step 1…

A: Given query is to find the increased in population.

Q: Find the area of the region bounded by the graphs of f(r) =-r² + 2x+5 and g(z) = 121|- %3D

A: Area bounded by the curves :  If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on…

Q: The table gives the U.S. population to the nearest million for selected years from 1950 and…

A:

Q: the tunchon: a certain check point is given by 30) 13 VE Find the, çar pesihon, St), af Assame that…

A: In this velocity function is given, so to find the position function we need to integrate the…

Q: Given | f(x)dx = 6 and | g(x)dx = 2 , evaluate 0.

A:

Q: Solve the following differential equations of >(3x² – 6.xy)dx +(-3x – 2y)dy = 0

A: