4. Find the equation of the tangent line and normal line that passes through the circle (x – 2)² + (y + 1)² = 10 at the intersection of lines x + 2y – 5 = 0 and 2x – y – 10 = 0

Q: Find the volumes OF the solid generated by revolving the regions bounded by the graph Of the…

A: Volume of revolution

Q: Find the directional derivative of f(x, y) = sin(x + 2y) at the point (-2, -3) in the direction 0 =…

A:

Q: Without solving for the undetermined coefficients, find the correct form of a particular solution…

A:

Q: Find T(t) and N(t) at the given point. r(t) = 11 cos(t)i+ 11 sin(t)j + tk; t= 2 T() - T N 2.

A:

Q: Suppose f(x, y)= g(x)h(y), where g and h are continuously differentiable functions of one variable…

A:

Q: 6) Determine constants a and b such that f(x) is continuous for all values of x. ax + 3, if x> 5 8,…

A:

Q: Find the equation of the line tangent to the graph of fox)= (In x) at x=8 (Type your answer in…

A:

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

A:

Q: Find the volume of solid generated by revolving the region bounded by the curve y=4/x' and the lines…

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

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

A:

Q: Use the Divergence Theorem to calculate the surface integral F• ds; that is, calculate the flux of F…

A:

Q: Evaluate F. dr F(x, y) = 5xi + 8yj C: r(t) = ti + v4 - tj, -2 sts 2

A: Calculate drdt. drdt=ddtti+4-t2j      =1i+124-t20-2tj      =1i+124-t2-2tj      =1i-t4-t2j…

Q: Part A: Design a function that meets the following criteria: The function must have both a…

A:

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

A:

Q: Find a plane through the points (-3,-1,-8), (-2,4,-7), (1,6,-4)

A:

Q: 19. inside * = 5sin O and outside " =2+sin0

A:

Q: (235 – 4.x25 + 2x)dx

A: The detailed solution is given below Thank you

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A:

Q: •5 f(x)dx = 6 and | g(x)dx= 2 , evaluate |3|

A:

Q: 2. Let f(x) = VI(2 – x)². Use the local linear approximation of f(x) at ro = 1 to estimate V0.99…

A: f(x)=x2-x2The linear approximation of f(x) at x0=1

Q: The solution to the indefinite integral 3. + 7x 1)dx is given by which of the following? Note: C is…

A:

Q: 1. A bumblebee was released and started to travel along a straight horizontal line. The directed…

A:

Q: Find the equation of the tangent to the graph of f(x) = x-3 at the point (5, 4). Start by evaluating…

A:

Q: 20.| sin³ }xcos" xdx

A:

Q: Time of Death Newton's Law of Cooling is used in homicide investigations to determine the time of…

A:

Q: the 1. For f(x) = r8/3 - 4x5/3, find a). the domain and f', b). f" (simplify f"), %3D c). the…

A:

Q: Describe the graph of the equation. r = 19 sin 17t i –- 19 cos 17t j O It is a parabola in the…

A:

Q: - In(a°y*) + x2 Consider z as a function of the variables x, y which is denoted by z and let P(1,-1)…

A:

Q: n2 series E(-1)"+1- converges or n3 +1 n=1

A: Given

Q: dy Then find the slope of the curve at the given point dx Differentiate implicitly to find…

A:

Q: 2. Find the absolute minimum and the absolute maximum of the function f(x) = x* – 4r³ +5 on the…

A: Given, f(x)= x⁴-4x³+5 ; [1,4] Finding the first derivative we have  f'(x)=df/dx= d(x⁴-4x³+5)/dx…

Q: Question 3 z+3 dx Use the substitution u = 1 - 2. 1 O sec I|+3 sin x+C OIn(1 – a) + 3 sin-1 a + C…

A:

Q: 8 Evaluate for (3x² -7x+4

A: We have to use the concept of derivatives

Q: Find the area of the region bounded by the graphs of the given equations. Enter your answer in exact…

A: Given :

Q: 22 r = 7 sin 0 + 50 cos O

A:

Q: II 2. 3. 2. 4. x² 1. X. 3. D3x 4. 1. Find the given derivative. 4-part 1 Homework: Homework Chap

A: Dx3x-12 + 4x32=Dx3x-12 + 4x-32                               =3Dxx-12+4Dxx-32…

Q: 11. Use the guideline in §4.4 to sketch the curve: f(x) = x² ln x. A). Domain, Symmetry, Asymptotes,…

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: If f(w) (7w), find f(w). Use exact values. COS f'(w) =

A:

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

A: Topic:- application of derivatives

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

A:

Q: A plane P, in R'is perpendicular to the vector n = (6, 2, 8), and contains the point (– 9, – 1, –…

A:

Q: Ise Stokes' Theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above.…

A: Using stokes' Theorem we have to evaluate given integral

Q: Suppose that z = f(x, y) is differentiable at the point (1024, 1024) withf,(1024, 1024) = 5 and…

A:

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: First I have changed the line integral into double integral with the help of Green's theorem and…

Q: Find the area with respect to y of the region bounded by xニy+2, ×=o, y=-! and ソミ2

A:

Q: You remove your pecan pie from the oven and place it on the counter for an hour before serving it.…

A: The temperature T in degrees Fahrenheit of pecan pie is modeled by T=f(t) where t is the time in…

Q: a) Find the arc length of the catenary y = coshx between X 0 and x = In4. b) Graph the functions y =…

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: 16 d :| (2V8– 1) dt da. valuate dr. dx 5.

A: We have evaluate to the given expression