4. Evaluate lim (cos x)¹/x². x-0

Q: 2 Let f(x) = ₂²5 on [-3, 1]. x+5 Find all numbers c in [-3, 1] for which the derivative is equal to…

A: We need to find values of c.

Q: Use the formula k(t) k(t) = ||r' (t) x r"(t)|| ||r' (t)||³ to find k(t). r(t) = 7 cos(9t)i + 7…

A: Let's find.

Q: f sin √x dx

A:

Q: A circle is centered at an angle's vertex. The angle's rays subtend an arc that is 6.6 cm long, and…

A:

Q: Show complete solution. Let S be the surface with equation y = (4x2/9) + z2 a. Write the equation…

A:

Q: Find the interval of convergence for xn 5n 8 n=0

A: The given series,     ∑n=0∞xn5n

Q: Solve the following X 1.0[₁-2x] i. D ii. D[xln (2x)] iii. D[cosx - 3 sin (2 x) ]

A:

Q: ad all values of x For w/c the graph of f lies above the graph of. f(x) = 49x; g(x) = 1

A: Given the query is to find the values fo x for which f is greater than g.

Q: Solve the following a) 2d²y_dy 3y = 25 sin 2x dx² dx d²y b) - 4 - 3y = 25 sin 2x dx² dx c) d²y dx² +…

A:

Q: dy (x + 1) dx = 1 x = 0; y=2

A:

Q: Verity Green's Theorem by evaluating both integrals ƏN [x² dx + x² αy = [] (2 - 0) A √y² dy dA ax ду…

A:

Q: The figure in this exercise shows a horizontal layer of the vector field of a fluid flow in which…

A: This is a problem related to vector field. Based on the formula and concept we will answer the…

Q: Find the absolute extrema of f on [-2, 3] if f(x) = x² - 6x - 1 O √5 O 2

A:

Q: 3. Determine whether each geometric series converges. If the series 7n+1 2n converges, find the sum.…

A: Let's find.

Q: Question Evaluate the indefinite integral given below. [ (sin³ (sin³ (x) - 3 sin² (x)) (sin (x) — 4…

A: Given,             ∫sin3x-3sin2xsin4x-4sin3x6cosxdx

Q: A pendulum of length 10 cm has swung so is radian measure of the angle formed by the pendulum and a…

A: Follow the procedure given below.

Q: Let S be the surface with equation given on the image. a) Write the equation of the traces of S on…

A:

Q: Find the derivative of 83-4 A. 3 ln 8 B. 83x-4 C. D. OA OB OD OC 83-4 ln 8 83x-43 In 8

A: We are authorized to solve only one question, please repost remaining questions Derivative of…

Q: ck < cre ISP Question af Calculate for the function f(x, y) = x² + y². dr Select the correct answer…

A:

Q: Consider the following series. Σ» (#1) (a) Determine whether the series is convergent or divergent…

A:

Q: Sketch the region enclosed by the curves à - 5 = 4y and x − 21 = (y — 4)², and compute its area.

A: x-5=4y⇒x=4y+5     x-21=(y-4)2 ⇒x=(y-4)2+21 Area between the curves…

Q: While measuring the side of a cube, the percentage error incurred was 3%. Using differentials,…

A:

Q: A company producing jigsaw puzzles has fixed costs of $7000 and variable costs of $4 per puzzle. The…

A:

Q: 2. Evaluate fy³ dx-r³ dy, where C is the circle of radius 2 centered at the origin, in the following…

A:

Q: An angle's initial ray points in the 3-o'clock direction and the angle measures radians. Which of…

A: We have to choose correct option

Q: S 7 tan (2x) dx 2 Hint: tan²x = sec ² x - 1

A:

Q: 49³y dx3 - 13 dy+ dx + 6y = 0

A: Since you have posted multiple questions i can do first question as per our company guidelines

Q: Find the centroid of the region by inspection and confirm your answer by integrating. (12,12) x = y…

A:

Q: 2. Find are Ətəx

A: The given function is v=(3t-x)e-2t ................................ (1)

Q: log(is²t) + 1 log; 10 + logn C logn, 10

A:

Q: Guess the value of the limit (if it exists) by evaluating the function at the given numbers. - 4x…

A:

Q: A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level and…

A:

Q: r₁(t) = 9ti + 4t²j + 3t³k, r₂(t) = t¹k d # [r₁(t) · r₂(t)] = = dt d dt [r₁(t) × r₂(t)] = r(t) x

A:

Q: Evaluate the given surface integral a) ff x² ds where S is the unit sphere: x² + y² + z² = 1 b) ff…

A:

Q: Find the volume generated by revolving about the y-axis the area bounded by the curve x^2 = 4(x-y),…

A:

Q: Determine the general equation of this differential equation. xy³ dx + e*dy = 0

A:

Q: The Bernoulli's form of the differential equation x²dy+ (2xy-y³dx=0 is The Bernoulli's form of the…

A:

Q: Find T(t) and N(t) at the given point. r(t) = 6 cos(t)i + 6 sin(t)j + tk; t = T() 6 37 0, √/3 X N…

A:

Q: A cylindrical can, open at the top, is to hold 800 cm³ of liquid. Find the height, h, and the…

A:

Q: Suppose that z = x³y², where both x and y are changing with time. At a certain instant when x = 2…

A:

Q: Let f(x) = 3x5 - 5x³.

A: As per our guideline we are supposed to be answer only first three subpart of the question you can…

Q: In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated by the…

A:

Q: 1- Sinx + Cos2y=0 dy dx

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

A: We have to find the surface area.

Q: In ( ;). Find for. z = ln Əz Əx

A: Given that       z = ln(x/y)

Q: ep 1 Begin by rewriting the integral into the following form. 1 1= du/dx u x² + 8x + 5 x³ + 12x² +…

A: To integrate..

Q: Find the area of the region between the curves y = x and y = x. Area between curves =

A:

Q: Describe the graph of the equation. r = − 17i + tj + (t²-1) k It is a parabola in the x = It is a…

A:

Q: Solve the differential equation de 4d³-13 +6y=0 dy dx

A: To solve the given equation.

Q: Determine the volume of the solid obtained by rotating the region bounded by x=(y−2)^2, the x-axis…

A: Given:        x=y-22 The volume of the solid obtained by rotating the region about the x-axis is…