Solve for the Partial Derivatives and total differential of each of the following function

Q: Find the Area of the Surface obtained by rotating the curve about the x - axis y = cosh x, 0 ≤ x ≤ 1

A:

Q: R(t) = (2 In|sec tl, sin 2t, cos 2t) Find the distance travelled by a particle along the curve…

A:

Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. (a) lim sin (2x6) sin(4x…

A: Explanation of the answer is as follows

Q: 2x²+x-2 (x + 1) (x²+1) dx = √ [+41 + x+ 2 If S A B 5 © €/ 5 D 4 E) None 5/2 B (2x) + C 1 x²+1 dx,…

A:

Q: Find a particular solution of as =10csc² 2t determined by s= 2 when t == . dt

A: dsdt=10csc2(2t)  s(π/4)=2 ds=10csc2(2t)  take integration both side

Q: [xv x√2x + 1 dx

A:

Q: example of properties of definite integral

A:

Q: The selling price P of an item is 100- 0.02x dollars, where x is the number of items produced per…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y = −10+ 6x - x², x = 1 and…

A:

Q: A company produces computers. The demand equation for this computer is given by p(q) = -5q + 6500.…

A:

Q: Find the average value of f(x, y) = sin(x + y) over a. The rectangle 0≤x≤ 1,0 ≤ y ≤ n b. The…

A:

Q: s Find the exact slope of the tangent line to the parametric curve π t = x = 9 cos(t) y = 4 sin(t)…

A:

Q: Function problem. Check that the following that is harmonic and determine is a harmonic conjugate. y…

A:

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bound by…

A: Volume of solid is evaluated using cylinderical shell method.

Q: A bank has decided to set its interest rates to compound monthly on all deposits in order to give…

A: We know the compound interest formula:A=P1+rnntwhere A=Principal amount +interest Amount…

Q: Find the area of the surface generated when the given curve just sayin revolved about the x-axis.…

A: SOLUTION-

Q: 2-1 4s - 4 s² - 16/

A:

Q: Evaluate the double integral: 3 +9 Lo L₂ Y COS(2 (Hint: Change the order of integration to dy dx.) y…

A: The objective is to evaluate the double integral.

Q: The volume of a cube is increasing at the rate of 4cm³/min. How fast is the surface area increasing…

A:

Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

A:

Q: the following function problem: check that the is harmonic and determine it it is a harmonic…

A:

Q: Find the derivative of the following functions. Use long method. a. f(x) = 3x² + 5x - 100 b. f(x) =…

A:

Q: Find the transition points. y = 4x7 - 56x6 (Use symbolic notation and fractions where needed. Give…

A:

Q: 4. Evaluate the line integral along the path C given by x = 2t, y = 10t, where 0 ≤ t ≤ 1. I (a) √(x…

A:

Q: Let line l : x=y/2=z/3 and point P(1,0,1). Find an equation of the plane (in point-normal form)…

A: Solution of given question is written in below steps.

Q: xdy = (5y + x + 1)dx Ans: y

A:

Q: ds Find the complete solution of = 8t³ √s. dt

A:

Q: The average number of vehicles waiting in a line to enter a parking ramp can be modeled by the…

A: Given, f(x)=x24(1-x)

Q: For the cubic polynomial function f(x) = : ax³ + bx² + cx + d, find a, b, c, and d so that 0 is a…

A: Solution :fx=ax3+bx2+cx+d f0=2  givend=2   ... 1critical number :f'x=0f'x=3ax2+2bx+c3ax2+2bx+c=0c=0…

Q: Solve ²₂(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

A: ∫-22(x+1)(x2+2)2(x2-1) dx

Q: x-4 x²+2x-15 Inx+51-Inx-31+ C 8 Option 1 S: dx 1 (x + 5)⁹1 Je In + C + x-3 -100 1 9 In|x + 5|ln|x −…

A: We can find the answer as below

Q: o - 23 dy

A:

Q: 1 Find the arclength of the curve x = 3 1 ',v = 22 -t³ t2 with 7 ≤ t ≤ 8.

A: The arc length of a curve in parametric form x=f(t) ; y=g(t) for b≤t≤a is given by,…

Q: Find the volume generated by revolving the area bounded by x² - 4x - 4y + 4 = 0 and y = 1 about the…

A: To find the volume generated by revolving the area bounded by x2-4x-4y+4=0, and y=1, about the line…

Q: (-1)k 9. Does the series Ex=1 +7 converge absolutely, converge conditionally or diverge? A.…

A:

Q: dy Find the complete solution of 2e-2 cosx- dx Note: fedu=e" + C - sin² x = 0.

A:

Q: 4. Verify the final value theorem for the function 3t²e-4t and determine its steady state value.

A:

Q: 1f S₁ (x+5) dx = Sº (x+5) dx = 14, then the value of b is equal to If A) None B 3 с 4 D -3 E 2

A: We have to find the value of b.

Q: Find the Area of the Surface obtained by rotating the curve about the y -axis y = √√x, 1 ≤ y ≤2

A: Given y=x13    1≤y≤2Rotating about y-axisarea of surface of revolution about tghe y…

Q: 5) ( cos 'x dx -1 Where: u = cos(x) dv = dx

A:

Q: Determine if the function f (x, y) = if (x, y) = (0,0) is continuous at (x, y) = (0,0). If not,…

A: Use limit to find wheather function is continuous or discontinuous.

Q: Use Figure 1 to evaluate each trigonometric function of angle A. The side adjacent to angle A has…

A: As we know that; The trigonometric ratios;…

Q: Find the surface area if C = {(x, y): 1 ≤ x ≤ 2,y = about the x-axis.

A:

Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

A:

Q: A bucket that has a mass of 25 kg when filled with sand needs to be lifted to the top of a 20 meter…

A:

Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

A: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

Q: 2x - 3 Examine the function f(x):= x²+4 from the point of view of monotonicity and give its local…

A: This question can be solved using the concept of monotonicity and local extrema.

Q: The paraterized curve below is rotated abour the x-axis. Find the area of the surface. x = cos³ (0)…

A:

Q: pair of parametr quations is given. x = e4t y = et (a) Sketch the curve represented by the…

A: