Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. lim x → 0  x2 3 − 3 cos(x)

Q: tdt 1-t4

A: Topic = Integration

Q: Evaluate the limit using L'Hospital's rule 14* – 3" lim

A:

Q: 3 In ДАВС, с % 15 ст, b — 4.6 ст, тLA: = 106°. Find the area of the triangle and round to the…

A:

Q: Find div F and curl F if F(x, y; z) = x°i – 7j+yzk. div F= curl F=

A:

Q: Problem 8. If the focus of a parabola is at (0, 4), and the directrix is y=-4, write the equation of…

A:

Q: xdx 41. 12-х

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

Q: S csc° 3x dx

A: This question is related to indefinite integration, we will we will solve it using given…

Q: v F= F=

A:

Q: A farmer finds that if she plants 90 trees per acre, each tree will yield 30 bushels of fruit. She…

A:

Q: dy Given a first order differential equation dx Зx* у + tan y x' +xsec' y Q3

A:

Q: Problem 5 Part 1: Consider a cost function where C(x) in Philippine peso is the total cost of an…

A: Let's find.

Q: Problem 7. Solve the equation logx+log(x+1) = log12 and leave your answer in exact value

A: Solve for the value of X

Q: 2. S CoSx+sinx-1

A:

Q: Consider the function f(x)=−3x2+30x−2.   a.   ​Determine, without​ graphing, whether the function…

A: Given; f(x)=-3x^2+30x-2

Q: Example 22 Find the eccentricity and directrices of the hyperbola given x? y? 1 9 16 Sketch the…

A: Given: x29-y216=1

Q: Finding the length of a curve. Arc length for y = f(x). Let f(z) be a smooth function over the…

A: To find the arc length of given function.

Q: Find the sum of the geometric series. 2.5 15 25

A:

Q: Find div F and curl F if F(r,y, z) = 1°i – 7j + yzk. div F= curl F=

A:

Q: 1. For the autonomous differential equation = y(4 – y²) find the equi- librium solutions and…

A:

Q: Find the limit. 421 (a) lim 7+ 17 (b) lim x-0 X 3

A: Topic = Limits

Q: Find the area inside the oval limaçon r=7+3 sin 0. The area inside the oval limaçon is (Tuno uor…

A: we have to find the area.

Q: 3. Let f(x) = x (x² + 1)/2. (a) Evaluate fo f(x)dx using integration by parts. (b) Evaluate f f(x)dx…

A:

Q: S V9x² + 64

A:

Q: dr Let A be the area of a circle with radius r. If dt dA = 2, find dt when r = 5.

A: Given :drdt=2r=5

Q: 1- r 3 Consider the lines l : 2 2 - y = z +1 and l2: = y –2= 3 1. Determine a direction vectors for…

A:

Q: 1 æ(ln æ)² de

A:

Q: dy 5 if y = 2x² + 5 and dt dx Find at x 4. dt dx dt

A: Solving the problem by finding the value.

Q: Зx* у + tan y dy Given a first order differential equation dx Q3 x' +xsec? (a) Clarify the exactness…

A:

Q: Find the divergence of the vector field F. F(x, y) 4xe*i 6x²y?j

A:

Q: View Policies Current Attempt in Progress Find r'(t). r(t) = (tan-(9t))i+t cos(t)j – Vik | NOTE:…

A:

Q: V3x - 2 lim tan- %3D x + V3

A:

Q: The average value of f f(x)dr if c =

A:

Q: Finding the work done in lifting a leaking bag of cement. A bag of cement originally weighing 143 lb…

A:

Q: 2)

A:

Q: (-1) ntl n=1 n3

A:

Q: Find div F and curl F if F(x, y, z) = 17y*z*i – 3x'2ºj – 3ry®k. div F= curl F=

A: Let's find.

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: The following series is divergent: (8")(10") (7")(9")+1' n=1 Select one: O True O False

A:

Q: sec(Inx) tan(Inx) dx

A:

Q: Find div F and curl F if F(r, y, z) = xz°i+ 2y°x²j+ 6z²yk div F= 2° + 16 y' x + 12 z Y curl F=

A: Given F(x,y,z)=xz6i+2y8x2j+6z2ykTo find div F & curl F:

Q: e equation (2 cose – 1)(3 + tane) = 0 over the interval [0, 27]. solving for trig functions,…

A: We will solve the equation.

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

A: we are given the function f(x)=cos(x) and the interval -π3,π3.The function f(x) is continous on the…

Q: answer

A:

Q: 1 Σ 6" - 5 n = 1 8

A: Given :

Q: Find V· (V x F) if F(x, y, z) = 2 sin xi + 2 cos(8x – 9y)j+ zk. - V · (V × F) :

A:

Q: Find the curvature and the radius of curvature at the point t = 0. e' cos(t), y = e' sin(t), = 3e* x…

A:

Q: Determine if the following series converge: 2.4.6 . · (2n) ... (a) (b) ) Inn 3.6 - 9 · · · (3n) ...…

A:

Q: Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x² – 3x + 8…

A: Here We have to use the definition of the derivative.

Q: Evaluate the limit using L'Hospital's rule ez – 1 lim z+0 sin(82)

A: Here I have appended the formula used in the solution part.

Q: What is the lim,→1 4x 7 .? x+1

A: limx→1 4xx+1The function is defined at x=1.limx→1 4(1)(1)+1limx→1 41+1limx→1 42=2