Find the length of the curve, L. y? = 64 (x + 5)* , 0< x < 3, y > 0

Q: Evaluate JJ xy dA, where R is the region in (1, 3) (5, 3) (2, 1) (4, 1)

A:

Q: Find the approximate area under the curve of f (x) =x+1 from x = 0 to x = 2, using 4 left-endpoint…

A:

Q: Find the area of the shaded region. y = -x3 + x2 + 16x and y = 4x %3D 30 254 20 IS 104 y 4x 20 25 30…

A:

Q: Determine the area of the region enclosed by y3x^2 and y=x^1/2

A: To find the area of the region enclosed by the given curves.

Q: Find the area of the region enclosed by x2 and y = 5x by integrating with respect to y. the curves Y…

A:

Q: Find the Taylor series centered at a = 0 for the following function: -7x f(x) = e 8. Answer: n=0 (Be…

A:

Q: Find ▽ x (▽xF) if F(x, y, z)=10xy j+ 10ryz k.

A: The value of ▽ x (▽xF) is (10 + 10y)i + 10xj + 0k

Q: Find the area of the region bounded by the graphs of f (x) = x° and g (x) = x. (А) 1 B c) 0.5 D 3

A:

Q: 1009 1010 Suppose R= E (2k) = 2 + 4 +6+.+2018 and S= D (2k-1) =1+3+ 5+.. + 2019 What is the value of…

A:

Q: 55-58 Use the properties of integrals to verify the inequality without evaluating the integrals. 55.…

A: Let's find.

Q: Evaluate the limit using L'Hospital's rule: Lim0+1 In(x+1) 2xe"

A:

Q: Consider the functions. f(u) = u³ + u g(x) = cos (x) Find the following function and derivatives.…

A: The given functions,fu=u8+ug(x)=cos(x)

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: Find the approximate area under the curve of f (X) =cos ( from x =0 tox=T, Using 4 trapezoids. 3 2.6…

A:

Q: (c) Sketch a graph of the path, and sketch the velocity and acceleration vectors at the given point.…

A:

Q: Finden- un) andrn - in twe dferent mays r(t) -n+ se's - e'N, wt) - t'k (a) re) - uch) () Find the…

A:

Q: 7-18 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7.…

A:

Q: Evaluate the line integral / (6x + 8y)dx + (4x – 8y)dy along the curve C: x = 2 cos t, y = 4 sint…

A:

Q: V4-x² c 3-x2-y² Evaluate the iterated integral. x dz dy dx -5+x²+y² A 128/15 в) 16/89 c) 23/6 6.

A:

Q: af Find for the function: f(x, y) = xcos(xy) + 2xy2

A:

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A:

Q: Determine which value best approximates the area of the region bounded by the graphs of f and g.…

A:

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: Volume

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A:

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

A:

Q: Use the Product and Quotient Rules as necessary to find the derivative of f(x) = 7x? cos(x) (Use…

A: The given function,      fx=7x2cosx

Q: y+1 - Z 4. Find the distance between the lines = z and x = 3 %3D -2

A: topic- distance between lines

Q: dy Compute the derivative y dx y = 5x4 – x-4 (Express numbers in exact form. Use symbolic notation…

A: Given,y=5x4-x-4  Formula: If, y=xn then, y'=nxn-1

Q: Question 10 Find the area of the region bounded by the graphs of f (x) = x° and g (x) = x. (А) 1 B)…

A:

Q: Question 14 Find the area of the surface that is generated by revolving the portion of the curve y=…

A: Given: y=x2⇒x= ±y Since , we are dealing with x=1 to x=2, we will take the positive value Thus, x=y…

Q: Edit Find div F and curl F if F(x, y, z) = 13y*z'i – 11x°2°j – 5xy'k. div F= 0 curl F= k (-55 a' 2º…

A:

Q: al)= gi+ sk vio)= 5), ro) 0

A:

Q: Let y = (3x + 2 sin(x))*. Find f(x) and g(x) so that y = f(g(x)) and compute the derivative using…

A: Here the given function is: y=(3x+2sin(x))4

Q: 2. Write the given (total) area as an integral! a. The area above the x - axis and below y = 4 -x2 T…

A: Area between the curve  y=f(x) and x-axis is defined as ∫abf(x)dx where a, b are point of the…

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 7x?y²j

A: Find the divergence of the vector field F.

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t'i+ t3j K(t) =

A:

Q: Find the principal unit normal vectóř tô thể curve at the r(t) = /2ti + e'j + e-k, t = 0 %3D

A: Principal unit normal vector

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction to PQ

A:

Q: Find the approximate area under the curve of f (x) = x< +1 from x = 0 to x = 2, using 4…

A:

Q: d d Calculate ri(t) · r2(t)] and [ri(t) x r2(t)] first by differentiating dt dt the product directly…

A:

Q: n/2 c sine Evaluate the iterated integrals J. r cos e dr de 0. A 1/6 B 1/2 c) 6 D) 11/9

A:

Q: Two particles travel along the space curves r(t)and u(t). (If an answer does not exist, enter DNE.…

A:

Q: Find V · (V × F) if F(x, y, z) = 10 sin xi + 5 cos(8x – 9y)j+ 4zk. V· (V × F)

A:

Q: Find V x (V × F) if F(x, y, z) = 4xyj+ 9xyz k. V x (V × F)

A:

Q: X+2 At what points is the function y = continuous? 2 X- 9x + 14 ... Describe the set of x-values…

A:

Q: Given h(r) = 1/r+3 find the following: (a)h(x2)= (b) h(x2 + 1)= (c)h(x2) + 1=

A:

Q: Find the Laplace transform of f(t) ={0, 0 ≤t ≤1         7t −7, t ≥1 .}

A: Given :f(t)=00≤t≤17t-7t≥1

Q: Find the exact arc length of the curve over the stated interval. 1 1 + from y = 1 to y = 3 x = NOTE:…

A: Aec length of the given curveL=∫131+dxdy2dy    Considerx=16y3+12y-1thendxdy=(16×3y2)+-12y2…

Q: ||r'(t) x r' r"(t)|| Use the formula k(t) to find k(t). 3 ||r(t)||* r(t) = t'i+ t5j K(t) =

A:

Q: For each of the following series determine if the series converges or diverges. 00 In(n) Σ n n=2 n3…

A: The given series,1. ∑n=2∞ln(n)n2. ∑n=0∞n3n4+1