If a person's temperature after x hours of strenuous exercise is T(x) = x³ (7- x²) + 98.6 degrees Fahrenheit (for 0 ≤ x ≤ 2), find the rate of change of the temperature after 1 hour. °F/hr

Q: 1-5th gaase rsino drdo

A:

Q: 32 Which one of the following is the general antiderivative G(a), for g(x) Note: CER Select one…

A:

Q: What is the limit of 3x4 as x approaches ? 1 2 12 evaluated 2 3 16 0 1 16

A: Given problem:- limx→12 3x4

Q: For the function y = (x - 2) lnx, what are the two x intercepts, and between the two intercepts, is…

A: The given function is y=x-2lnx. For x intercepts we take y=0 and then we solve for x. If y''(x)>0…

Q: the base radius and height of a right circular cone are measured as 10 cm and 25 cm, respectively,…

A:

Q: The graph of f is given below. -2.5 -2 -1.5 Why is f not differentiable at = -1? Of has no tangent…

A:

Q: Solve the differential equation where y = 8 when = 0. y + 3y x + 3 = (x+3)8

A:

Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A: This question can be solved using the concept of Laplace transformation.

Q: Determine whether the differential equation (4x² − 2xy + 6) dx + (2y² − x² + 4) dy = 0 is exact. If…

A:

Q: The speed of sound traveling through ocean water with salinity 35 parts per thousand has been…

A:

Q: For a particular function, the derivative is given by f'(x) = (x+3)(x-1)². Determine the x-values…

A: Topic = Derivative

Q: Let y = f(x), where f(x) = 7x³ + 3x. Find the differential of the function. dy = X

A: The differential of y is the derivative of the function times the differential of x,

Q: Evaluate the given limit. Show your complete solution. limo(-x ln(sin(4x² - x)))

A: Let's find limit of given function.

Q: e ☺ x +9 x² + 9x + 18 -dz

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: Find an antiderivative for each function when C = 0. a. 1 b. 2√x 1 c. ²{√x + 7/7 C. a. The…

A: Formula ∫ xn dx=(x(n+1))/(n+1) +c

Q: Which of the following is NOT TRUE about the tangent line intersecting the graph of a function? The…

A:

Q: b) Maximize the volume of this rectangular box. c) What are the dimensions & volume of this largest…

A: Solved below.

Q: Determine the area of the region enclosed by the curves y - 3x = 2 and 2x² - 4-2y = 0. Do not…

A:

Q: What is the limo+ sin(y) In(y)? For answers write... that are in decimal form and round off to…

A:

Q: _z = g(x,y)=√x² +2y²

A:

Q: Find the area of the triangle in IR³ that has vertices P₁= (1, 0, 1), P₂=(2, 3, 1) and Ps= (0, 2,…

A:

Q: Using the concept of the derivative of sin x, what is the antiderivative of sin x? -2 cos x + C 2…

A: We know that: ddx(cos x)=-sin x...(1)

Q: Find the antiderivative for each function when C equals 0. Do as many as you can mentally. Check…

A:

Q: 4. y +==y² A.-4-2 5. 4x² + 4y2 = 36 A. - 6. x² + 3xy-y = 7 A. 2x-3y 3x-1 B. 3 B. 4y-2 KIA 2x+3y 3x-1…

A:

Q: Which function is Chain Rule most useful for? Composite function Polynomial function Logarithmic…

A: In Differentiation chain rule is important tool for differentiating composite function .

Q: How many asymptotes (both vertical and horizontal) does the following function have: sin(x) -?…

A: To determine the number of asymptotes for the given function.

Q: What is f 5√xdx? 3 f 5√√xdx = 5x² + C 2 3 f5√xdx = 10x² + C 3 f5√xdx = 5x² + C 3 [ 5vxdx= 5x? +C

A: Let's solve given integral.

Q: what is y' of y=sin-1(cos x)

A:

Q: 2.) Determine whether the geometric series is convergent or divergent. If it is Σ(13) " n=1…

A: To determine  whether the given geometric series is convergent or divergent. If it is convergent, to…

Q: Use the graph below to determine that slope of the secant line on f(x) from x-1 to x-3. 5 4 3 2 y =…

A: use the graph for finding the slope of the secant line.

Q: Evaluate: limt o sin 3t t5 (t-1)² using L'Hôpital's

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 10 5(5+10) a/n A ナ B 5+10

A: See the details solution in below

Q: What is S (x² + 2x)² dx? + x³ + ³x² + C 4 S (x² + 2x)²dx = ¹x¹ + x³ + 4 f (x² + 2x)²dx = (x² + 2x)¹…

A: We know, ∫xndx= xn+1/(n+1)

Q: A. Find the volume generated by rotating the region bounded by y=x, y=1 and the y-axis rotated about…

A:

Q: Identify and sketch the graph of y = x² + 1 in R³.

A: Given:

Q: Verify the product law for differentiation, (AB)' = A'B + AB' where A(t) = To calculate (AB)', first…

A:

Q: Q4/ Answer two from the following :- 4- Evaluate and change the order of integration in 1 = ²*xy…

A:

Q: 0 Given the piecewise function f(x) = 5-x 5-z What is f (4) ? Answer: f4 (4) = What is f¹ (4) ?…

A: Given function:-

Q: What is the derivative of x² + y² = 9 using mplicit differentiation? dx = xy dy dx = -xy dy dx dy dx…

A: Given query is to find the derivative of the expression.

Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A: A detailed solution is given below.

Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A: Given x=t-4To find L{x.e-x}

Q: x/8 sin 3r cos 5r dr

A:

Q: 10. Prove that any cyclic group is abelian.

A: As you are asked multiple questions but as per our guideline we can solve only one. Please repost…

Q: Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1.

A: The function f(x) is given by, f(x)=ln(3-2x) Differentiating the function successively upto n…

Q: 3t 2t - 1 1-t 1+t [][] 3 and B(t) = 51² 51³ t Verify the product law for differentiation, (AB)' =…

A: See the details solution in below

Q: UT 5 4 3 2 1 Find lim f(x) 3 05 2 04 O Does not exist 2

A: Given

Q: Convert ₁(4-4x²-y2)dyda into a triple integral with dV = dydzdx.

A:

Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the…

A: The objective is to solve the above question.

Q: Find the solution of the given initial value problem. π ty' + 2y = sint, y "(-) = 5, t > 0 Y ||

A: Concept: linear differential equation of the form dydx+Py=Q The general solution of the linear…

Q: What is the derivative of y = sin (x³ sin (x³ – 3x)?

A: