d d Calculate r:(t) · r2(t)] and r:(t) × r2(t)] first by differentiating dt dt the product directly and then by applying the formulas d r:(t) - r2(t)] = r:(t)- dr2, dri dt r2(t) and dt dt d dr2, dri ri(t) x r2(t)] = r¡(t) × x r2(t). dt dt dt r1(t) = cos(t)i + sin(t)j+3tk, r2(t) = 2i + tk d ari(t) - r2(t)] =| d ri(t) x r2(t)] : dt

Q: The point (– 1, 3) is on the terminal side of 0 in standard position. The exact value of cos(0)is…

A:

Q: Question 15 1-sine Evaluate the iterated integrals J. J. p2 cose dr de̟ A 1 В) 2

A: ddθ(sinθ)=cosθ ∫rndr=rn+1n+1, for any real number n.

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

A:

Q: 2. Determine whether the statement is True or False. If it is false, explain what makes it false, or…

A:

Q: 3. The derivative of /(x) = In x at x = 3 when hourrent = 0.001 and hprevious = 0.002

A: Given problem:- 3. The derivative of f(x) = In x at x = 3 when hcureent= 0.001 and hprevious = 0.002…

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

A:

Q: Find the exact arc length of the curve over the stated interval. 1 1 +y2, from y = 1 to y = 4 x = 4°

A:

Q: Use any method to simplify the complex fractloh. k+1 25k 3k - 1 15k

A: Use the fraction rule; abcd=a·db·c   The given expression is: k+125k3k-115k

Q: Consider the following. f(x) = x* – 4x² g(x) = x² - 4 (a) Use a graphing utility to graph the region…

A:

Q: Use the arc length formula to find the length of the curve y = 3x - 5, -2 SxS 3. Check your answer…

A: This question is related to Functions and curves, we will solve it using given information.

Q: bounded by the graphs of the equat y

A:

Q: Question 2 Use spherical coordinates to find the volume of the solid. The solid enclosed by the…

A:

Q: If e is an angle in standard position, Cot(@) > 0 and sec(e) <0, then the terminal side of 0 lies in…

A: Trigonometry

Q: Question 2 Use double integration to find the volume of the solid bounded by the paraboloid z = 9x2…

A:

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere x² + y?…

A:

Q: first octant 2 4- x+y dy dx -

A:

Q: Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 А) 6 в) 9 c) 12 D)…

A: Volume

Q: Perform the indicated operation. Simplify if possible. b2 64 b+8 b+8

A: To simplify the given expression.

Q: 1. Determine whether the series is convergent or divergent. If it's n=l e"+1 convergent, find its…

A:

Q: Using the method of cylindrical shells, set up but do not evaluate an integral for the volume of the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use double integration to find the volume of the solid bounded by the paraboloid z = 9x2 + y?, below…

A:

Q: 1- Show that the following subset is a subgroup. H = {o e S, lo(n) = n}cS,

A: Explanation of the answer is as follows

Q: Evaluate J xy dA¸ where Ris the region in y =x? 2 A 13/7 16/3 18 D) 20 B.

A: To find : ∬xydA where  R is the region of y=x2 and y=0

Q: Find div F and curl F if F(x, y, z) = 13y*z'i – 11a'2®j – 5xy*k. div F= curl F=

A: We can solve as follows

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: 11 Evaluate the iterated integral. JJ, J, (x² + y² + z?) dx dy dz A 5 в) з D 10 00

A:

Q: Find the divergence of the vector field F. F(x, y, 2) = In(9x+ 8y² )i + 72xyj + In(8y² + 5z? )k #6…

A: Solution is done in step 2 and 3

Q: 2. Determine whether the statement is True or False. If it is false, explain what makes it false, or…

A:

Q: find the equation for x in y=3x-x^3

A: Solving

Q: Sketch the region of integration. (Select the correct graph.) rIn 6 6 dy dx In y y y 61 6 4 3 2 1 4…

A: Area

Q: Evaluate the definite integral. 9ti +3t'j + Vtk) dt

A: The given integral,          ∫-119t i+3t3 j+t3kdt

Q: Question 14 1. 2 Evaluate the iterated integral. J, J. J. (x²+ y² + z?) dx dy dz -1°0 (А) 5 (в) з D)…

A: To find following integral valueI=∫-11∫02∫01(x2+y2+z2)dx.dy.dz

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 4 cos(t)i…

A: To find unit tangent vector at given parameter.

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: Find V· (V × F), if F(x, y, z) = 7e*²i+ 6xe"j –- 6e²k. V·(V × F)

A:

Q: Find the area of the region bounded by the graphs of f (x) = x³ and g (x) = x. A 1 B) 4 C) 0.5 D 3

A: Solution is given below:

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: 'ind the area of the region that is enclosed by the cardiod = 20 + 20 sin 0. OTE: Enter the exact…

A:

Q: Question 3 Express the area of the given surface as an iterated double integral, and then find the…

A: Let's find.

Q: Sketch the region R of integration and switch the order of integration. F(x, y) dy dx y 2 2 -4 -2 2…

A:

Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating d dt dt the product directly…

A:

Q: Use the arc length formula to find the length of the curve  y = 3x − 5,   −2 ≤ x ≤ 3.  Check your…

A: Given : y=3x-5 ,   -2≤x≤3   To Find : Arc length

Q: Find the area of the region inside the circle r = 24 sin 0 and outside the cardioid r = 8 + 8 sin 0.…

A:

Q: Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the…

A: We need to set up and evaluate integral.

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1…

A:

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

A:

Q: 1. Find the equation of the tangent line to the curve x = e', y = et at t = 1.

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

Q: Find the unit tangent vector to the curve at t r(t) = t°i + 3t?j, t= 2 T(2) =

A:

Q: xe*y dy dx

A:

Q: find the differential dy. Hence, estimate the value of 1+ (1.023 2H y =

A: