8. What is the domain and range of the following relation? y=x²-2x-3 y 5 8 X

Q: Find foda + C

A:

Q: Find d dr (73 (7²). Type In(x) for the natural logarithm function.

A: As we know that; The Power law: ddxxn=nxn-1 And the common derivative; ddxlnx=1x   Let, y=7x

Q: Solve the following first order differential equation: dy y² +49 +3 35 4 x² + 2x³-3x² dx == 0 given…

A: Differential equation: 35x4+2x3-3x2·dydx-y2+49x3=0

Q: Let f(x) = ln(x² + 16x + 68) f'(x) =

A:

Q: Write the following expression as one integral. 3 5 3 [ -6 f(x) dx + f(x) dx - f(x) dx 0 0 3 5 3 $…

A:

Q: Find fxy(x,y) if f(x,y) = (x² + y²) 7. fxy(x,y) = ...

A:

Q: Find fxy(x,y) if f(x,y)= e 8xy² fxy(x,y)=

A:

Q: Find the curvature of the curve r(t) = (-1-4t, 2-t, 4 - 4t) at the point t = - 1. Check Answer

A: We know that curvature of a curve is given as: k=||r'(t)×r''(t)||||r'(t)||3

Q: A supermarket sells two brands of granola: brand A at $p per pound and brand B at $q per pound. The…

A: We have to find partial derivatives and new values of x and y .

Q: Let r(t) = (-5t¹-2, - 5e³t, 2 sin(3t)) Find the unit tangent vector T (t) at the point t = 0. Round…

A: This question is related to differentiation, We will solve it using given information.

Q: Evaluate the integral: Fa ○ x = 6 sin(0) ○ x = 36 tan(0) 28 x²√x² + 36 dx (A) Which trig…

A:

Q: Calculate the definite integral by referring to the figure with the indicated areas. d d a f(x) dx…

A: Solution

Q: Use calculus to find the open intervals on which the function f (x) = x +4√1 − x is increasing or…

A:

Q: Find the area of a triangle PQR, where P = (-1,-1, 1), Q = (4, -3, -6), and R = (1, -6, -3) Check…

A:

Q: 3. Including all steps, charts, and derivations details, use the curve sketching methods to sketch…

A:

Q: 4. The graph of f' (x), the derivative of f of x, is continuous for all x and consists of five line…

A:

Q: 1261 (2x+1 dz 4-3x -x² 1 (((x+) dx (3) 28 (2x-3 dx √(x²-1) (2x+3) 31 32 33 dx √(x²+1) (2x+1) alx…

A:

Q: Find 13 sin(82)da [13 sin(8x)dz = +C

A:

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A: Given: ∫05|10x-5|dx

Q: Q1. Find the equation of sphere with center (1, 2,-1) passing through the point (-1, 2, 1).

A:

Q: Solve the differential equation xdy]=0 xdx +sin? (%) [yde 4x ln || - 2y + x sin ( ² ) = 0 2x a. 2y…

A: Given :   xdx+sin2yxydx-xdy=0

Q: Q2. Find the second order partial derivative of x² - y² + 2xz - xy + yz.

A:

Q: Find the following limit. lim

A:

Q: 5. Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and…

A:

Q: Use L'Hopital rule, find the following limit? lim (4x + 1) cotx x→0+

A:

Q: Answer the following True or False. If g(x) is a continuous function and h(x) is differentiable such…

A:

Q: SEND IN 20 MINUTES PLEASE !!!! Find all extreme points (maxima, minima, saddle points) of…

A: Extreme points of the function fx, y=2x3 + 2y3 - 9x2 +3y2 - 12y

Q: Consider the function f(t) = 10 sec² (t) - 3t³. Let F(t) be the antiderivative of f(t) with F(0)…

A:

Q: Find fxy(x,y) if f(x,y) = (x² + y²)6.

A:

Q: The regions A, B, and C in the figure below are bounded by the graph of the function f and the…

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 10 - 5t, where 0 ≤ t ≤ 1.5…

A: The answer as follows:

Q: a. b. C. d. e. x² + 4x + 16 2 x² + 8x + 8 2 x² + 8x + 64 +2 x² + 4x + 5 2 x² + 8x + 16

A: Observe the mixed term and then guess the possibilities.

Q: Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented…

A:

Q: x² yey lim(x,y)→(0,0) x4 + x + y²

A: To evaluate the following limit.limx, y→0, 0 x2yeyx4+x+y4

Q: Find the Taylor series generated by f(x) = 6 sin 5 at x = 0.

A: Answer is in next step.

Q: Find the point at which the line y(t) z(t) = 2 + 4t -6-8t intersects the yz plane. 6-7t

A: The line x(t)=2+4t, y(t)=-6-8t, z(t)=6-7t intersect yz plane Note:    Multiple questions are given,…

Q: For the function f(x,y) = 5x² + 6y², find f(x + h,y)-f(x,y) h 11 f(x + h,y)-f(x,y) h

A:

Q: 3x³-28x² +40x-42 3x² - 4x+5 dx

A:

Q: Find the area S of the shaded region in the figure if ƒ (0) = 0² + 30. Note that 0 varies from 0 to…

A: To find the are S of the shaded region in the figure if fθ=θ2+3θ Note that θ varies from 0 to…

Q: IN 15 MINUTES PLEASE calculus Find all points on the curve x^2y^2 + xy = 2 where the slope of the…

A: Solution is done in step 2

Q: 10. Explain what it means if a. 6 = 0

A:

Q: Let P be the set of positive real numbers. One can show that the set P³ = {(x, y, z)|x, y, z € P}…

A: The objective of the question is determine the vector .

Q: = Using calculus, find the absolute maximum and absolute minimum of the function f (x) [-3,2].…

A:

Q: Evaluate £¹₁7 x8 − 7 x³ + 7 x² dx. Round your answer to two decimal places. £²₁7 r8 − 7 x³ +7 r² dr…

A: Given definite integral is: ∫-11(7x8-7x3+7x2) dx

Q: I have a question about the problem solved…

A: The explanation of your query can be solved using the concept of function.

Q: Let f(x) = 10x + 12 - 9e. Then the equation of the tangent line to the graph of f(x) at the point…

A: given f(x)=10x+12-9ex

Q: x Cothx Y = (Sink x) 4 Find dry" dx [ Sin'x]

A: Given: y=sin hxx cot hx

Q: sec 2(t)- 9t2 Justify your response. b. Find the antiderivative of f(t) = s

A:

Q: Compute the given integral. fcos¹ a a sin ædx = +C

A: Our Aim is to evaluate the integral given below:-∫cos7 (x) sin (x) dx -(i)

Q: Rewrite sin(x+ H Enclose arguments of functions in parentheses. For example, sin (2x). sir 20 in…

A: