3. Determine the point(s) where the function y = ₁ , has a maximimum and/or a minimum. Find BOTH coordinates and wirte the answer in EXACT form. You must use the First Principles Formula. [TH-7]

Q: 16 x0.67.dx

A: Formula  ∫xndx=xn+1n+1+c

Q: Screenshot (16 Find the solution of the given initial value problem in explicit form. 1 y' = (1 -…

A:

Q: Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate…

A: here the given differential equation  (6 -20y +e-5x)dx -4dy = 0 this can be written as  dy/dx +(5)y…

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A:

Q: 2 Short response Question 9. (Some formulas from Euclid in coordinates) Include pictures for each…

A: (1) d(x) = (x-a)2+(mx-b)2 we know the distance between (x1,y1) ,  (x2,y2)  is x2-x12(y2-y1)2

Q: 1. By eliminating the parameter t from the following parametric equations, find an equa- tion in…

A: As per the instruction, we will be answering the first one. For (a), Given: Now,…

Q: Verify Green's Theorem by evaluating both integrals for the given path. + ON ax C: rectangle with…

A: In this question, we want to verify the green's Theorem.

Q: 77% 77%

A: Given: F(x,y) = 6i-2j

Q: Use the formula k(t) k(t) = TEREST {|r' (t) × r"(t)|| ¡|r' (t)||³ r(t) = esti + e-tj to find (t).

A: The given curve rt=e5ti+e-tj

Q: Find curl (82 i + 9x j + 6y k). curl (82 i + 9x j + 6y k) = = ( )k )i + (i )j + (

A: To Find : curl(8z i + 9x j +6y k)

Q: Find curl curl (5z i + 6x j + 8y k) i 5 i i 6 (5z i + 6x j + 8y k). 8 = ( )i + ( )j + ( )k

A: Given that a vector 5z i^ + 6x j^ +8y k^ We have to find a curl of this given vector. Curl of a…

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Given,           ℒ-11s2+1s2+25

Q: curl(9z i+ 10x j + 4y k). (9z i+ 10x j+ 4y k) = ( i Textbook and Modia )i + (i )j + (i

A: To find out the curl of the given vector.

Q: Evaluate the line integral C: y² = 27x from (27, 27) to (0,0). NOTE: Enter the exact answer. 6-₂…

A:

Q: 0 xsin2x x² + 3 -dx =?

A: Given: ∫0∞x sin2xx2+3dx

Q: If r(t) = (e³t, e-4t, t), find r'(0), T(0), r"(0), and r'(0) x r"(0). r'(0) = II T(0) = r"(0) =…

A:

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = y""+ 2y" - y' - 2y =…

A:

Q: Find f such that f'(x) = f(4) = 44.

A: Given,            f'x=9x , f4=44

Q: Describe the graph of the equation. r = 18 sin 27 i+ 18 cos 2t j It is a circle of radius 18 in the…

A:

Q: ll is thrown vertically upward from the top of a building (when t-Oseconds). It has a height functi…

A: Topic:- application of derivatives

Q: ad curl F if F(x, y, z) = xz7i+ 5y¹¹x²j + 6z²yk. d with CamScanner

A:

Q: 1 *{{37² +3=6} S

A:

Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 15 inches above the…

A:

Q: Solve the given Bernoulli equation by using this substitution. O O O y = ± y = ± y = ± y = ± y = ±…

A:

Q: Let f(x) f'(x) = 3 sin r 2 + cos x Find f'(x).

A:

Q: Find the value of() for a solution (x) to the initial value problem: y"" − 3y" + 4y' – 2y = 0; y(0)…

A: In this question, we want to solve the third order homogeneous differential equation.

Q: Determine all critical points of the function f(x) = 2x(4- x)³.

A:

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y - 5xyz + 10yz²…

A:

Q: Find V (V x F), if F(x, y, z) = 6ei +9rej - 7ek. V. (V x F) =

A: To find ∇·∇×F, if Fx, y, z=6exz i+9xey j-7eyz k.

Q: Find the volume of the region bounded above by the sphere r = 2a cos0, and below by the cone = a…

A: Given: the sphere r=2a cos theta , cone ϕ=α0<α<π2

Q: Calculate the indicated Riemann sum S3 for the function f(x)=x²-9x-52. Partition [0,6] into three…

A:

Q: Use the graph to determine the intervals on r concave downward. 10 4 1.5 X 10 а.

A: Here we have concave upward and concave downward.

Q: Find div F and curl F if F(x, y, z) = 7evi-4 cos yj+ 10 sin² z k. div F= curl F

A:

Q: r = 17 sin 2t i - 17 cos 2t j

A: Given equation r= 17 sin 2t i- 17 cos 2t  j

Q: Given: f(t) = 3t4 + 6. Evaluate: F(3) Use 2 decimal places. 2.30

A: Here we have to apply laplace transform.

Q: Given: f(t) = 8 sin23t. Evaluate: F(1) Use 2 decimal places.

A: f(t) = 8 sin23t.

Q: 1 1 0.104 = x Use linear approximation, i.e. the tangent line, to approximate as follows: Let f(x) =…

A: Solution : Given that

Q: Express the following function in terms of unit step function and hence find their Laplace…

A:

Q: 3. Pedro walks at te speed of 40 meters/min from the school to home, by taking the longer route of…

A: Pedro walks at the speed of 40m/min from the school to home,by taking longer route of 100 m to the…

Q: Find the Wronskian of the functions f(t) = et sin(t) and g(t) = et cos(t). NOTE: Your answer must be…

A:

Q: ******* +70+ -10 -8 -6 -4 -2 ✔ +10+ y H 6 8 10 Q Write the standard equation for the hyperbola…

A: Given,

Q: 2. Reparametrize R using the arc length as parameter from the point P(-1, √37,5).

A:

Q: 4. an = 6n 5. a = 6. 2n+2 a = (-2)n-2n

A:

Q: Find the derivative of the function. f(x) = arcsec(4x) f'(x) = 4 4π√ 16x² - 1 :or 1 xV 16x²-1 2

A: Topic = Derivative

Q: Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

A:

Q: Find the limit, using ALGEBRAIC techniques written down (not just by graphing): lim x →9 √x - 3 X -9

A:

Q: Screenshot (1603) p Find the solution of the given initial value problem in explicit form. ³(²-) =…

A: Let's find general solution of diffrential equation.

Q: 2. (2xy-tan y) dx + (x²-x sec² y) dy Answer: x²y - x x tan y = C. = 0

A:

Q: The function f(x) = = The smaller one is x = 2x³36x² + 192x - 1 has two critical numbers. and the…

A: The given function fx=2x3-36x2+192x-1

Q: = √x³ + 2x³-3x d (x²+1)³ dx

A: Topic:- application of integration