Find the exact length of the curve. x=e'−t, y=4e¹/2, 0≤t≤2

Q: Evaluate the derivative of the given function at the given point. y = 2x³-3x² + x + 8; (1, 8)

A:

Q: If f'(x)=0 for all *, then a) f(x)=(x) for every x₁ x₂ c) f(x)>(x) for every x₁>x₂ d) f(x)>(x) for…

A: If  then which option is correct .

Q: Find the average rate of change of y with respect to x from P to Q. y= x²+ 7; P(5, 32), Q( 5.1,…

A:

Q: Calculate S3, S4, and S5 and then find the sum for the telescoping series S ∞ 1 1 =2(+2) Σ n=4 n+1…

A:

Q: Identify the inflection points and local maxima and minima of the graphed function. Identify the…

A: Given:  To Find:To identify the inflection points and local maxima and minima of the graphed…

Q: Need help understanding please and thank you

A: Summary: (7.Answer): arctan(x/2)+C (8. Answer): 2/3 * arcsin(3y) + C  or -2/9 (sqrt. 1 - 9y2) +…

Q: 7 63 tan (a+b); cosa for a in Quadrant III and sinẞ: for ẞ in Quadrant IV. 25 65 tan (a+B) Find the…

A: tan(α+β)=−162457​Explanation:

Q: Website Profit You operate a gaming website, www.mudbeast.net, where users must pay a small fee to…

A: explained below Explanation:Step 1:(a) Construct a linear demand function for your website and hence…

Q: Consider the logarithmic function: g(x) = 3 log2 (1-x) - 6 d) Sketch the function using the method…

A: Check explanation Explanation:Problem:Consider the logarithmic function:g(x) = 3log₂(1 - x) - 6d)…

Q: Let a (5, 1, 1) and b = (- 5, 1, 2). Find a × b. x V A

A:

Q: Are the areas of the two shaded regions below the same? f(x) = 1 (1+x²)2 y 1 1 0 I IT 4 g (0) = cos²…

A: To find the area of shaded regions

Q: Let h(x)=√(-4(t-2)² +8)dt. Where does h(x) have a relative minim

A:

Q: Find f'(x). f(x)= 2x 29+ In x

A: F′(x)=(29+lnx)22lnx+56​Explanation:If you have any problem let me know here in comment box for this…

Q: proved dy 2(x+1) ax if y = x²+x-10 x-z

A:

Q: On what interval(s) is the function f(x) = x - 4x³ both decreasing and concave up? (Enter your…

A:

Q: (d) Horizontal asymptotes. (e) Intervals where f is increasing and decreasing. (f) Local minima and…

A: Given: To Find: To determine the following: (d) Horizontal asymptotes(e) Intervals where f is…

Q: -312-6x+5=-10

A: The given equation

Q: Please help me with this, Look at the image Question: what are the x-coordinates of all points of…

A: The objective of this question is to find the x-coordinates of all points of inflection of the…

Q: I need help with this problem and an explanation for the solution described below (Discrete…

A: The objective of the question is to find the negation of the given statement. In logic, the negation…

Q: lim x-0 √x+5-√5-x χ

A: To find:-

Q: = Suppose that a continuous income stream has an annual rate of flow f(t) 700e-0.052 (in thousands…

A: Given:a continuous income stream has an annual rate of flow  in thousands of dollars per year.To…

Q: Complete the parametric equations of the line through the point (-6,1,-3) and perpendicular to the…

A: Point: (-6,1,-3)Plane: 6x-2y+2z=5

Q: 1. f(x) = (4x2)5

A: As per our guidelines we can answer only 3 sub parts of the given question so kindly repost the…

Q: For f(x)dx = lim f(x," )Ax,, determine the value of Axi. √²₁₂ max Ax, 0 Ola n 21˚ O O n 4-0 O O >18

A:

Q: If z = tan (金) and x = u² + v² and y = u² – v², find the - following partial derivatives using the…

A: Formula for the total partial derivative is given as follows

Q: ← The position of a particle in space at time t is r(t) as shown below. Find the particle's velocity…

A:

Q: If F(x) = f(xf(xf(x))), where f(1) = 3, f(3) = 4, f'(1) = 4, f'(3) = 5, and f'(4) = 6. Find F'(1).…

A:

Q: Let s(t)= v(t) == 6+3 + 45t² + 108t be the equation of motion for a particle. Find a function for…

A: We need to find velocity and acceleration.

Q: Evaluate 4x cos(y²) dy dr. 0

A: The value of integral is sin(16).Explanation:Approach to solving the question:Given question is a…

Q: Let f(x) = x|x|. (a) Sketch the graph of the function. 2 y У 4 2 2 y 4 2 y X y X J -4 -2 -2 2 -4 -2…

A: a)4th graph is correct answer b) Differentiable for all real x  c) f′(x)=2xExplanation:

Q: Evaluate the integral

A: 1.  3(arctanx)3​+C2.  earcsinx+CExplanation:

Q: Find all the values of x such that the given series would converge. n=1 (x-6)" 6n The series is…

A:

Q: Csc (2x)-2=o Four smallest solutions

A: Given that the equationcsc(2x)-2=0 we have to find the solution

Q: Solve by method of sines and cosines f3e3x sen² (e3x) dx

A: Since you have asked multiple question, we will solve the first one for you. If you want any…

Q: 2. Write an equation for sine and cosine for the graph below. 5. 0 5 10 15 20

A: We have given a graph of the function and we have to find the corresponding sine and cosine function…

Q: Given the graph of f(x) below, choose the correct option. A. f(x) is decreasing from A to C   B.…

A: Given:a graph of function f(x) with 4 points on graph A, B, C, and D.To find:behaviour of f(x) over…

Q: Use a linear approximation (or differentials) to estimate the given number. e-0.01 Need Help? Master…

A: Given that  consider the function Linear approximation of f(x) about the point x=a is given by now,…

Q: Joxe 4x dx = +C

A:

Q: Using: Higher order linear equation with constant coefficent / Homogenous Please Solve this equation…

A: The given equation is a third order linear differential equation with constant coefficients. The…

Q: The Taylor series

A:

Q: Consider the following higher degree polynomial function f(x): = -2x² (5-2x) (x² + 1) . d) State the…

A: DETAILED SOLUTION IS PROVIDED BELOWExplanation:…

Q: f(x) is f(x) is Consider the function f(x) = x²-4x + 3 on the interval [0,4]. Verify that this…

A:

Q: Given that f(x) Lπx) dx = 6 and [F(x) (a) L₁ F(X 0 f(x) dx f(x) dx = 9, evaluate the following.

A:

Q: Let ā = (−4, −5, −3) and 6 = (-5, −4, 4) Find a × 6. V >

A:

Q: math help

A: see explanationExplanation:Step 1: Step 2: Step 3: Step 4:

Q: (a) Domain of f(x). (b) r-intercepts and y-intercepts. (c) Vertical asymptotes and holes. (d)…

A: Here we have given a function: .

Q: 3. Verify the linear approximation at (0,0). 1 (a) ≈x+y1 x+1 (b) e cos(xy) = x + 1

A: To verify the linear approximation at

Q: 1. f(x) = (4x2)5

A: As per company guidelines for a question posted we are allowed to solve only first three subparts…

Q: Q7 Continuity 1 Point Let f(x) = x - 1 if x 1 x22x3 - 2x if x 1 Find the value of c for which f is…

A: for c=49​  f(x) is continuous Explanation:Step 1:Step 2: Step 3: Step 4:

Q: Verify the identity. Show that cos (p+q) cos (p-q) = cotp cotg - 1 cotp cotg+1

A: Need to verify the identity.