10. SHOW ALL WORK Verify the following identity:1 (1 - csc²0) (1 + tan²0 ) = tan² an evels to sty swan 10200x of eu SVETO

Q: Find the indefinite integral. (Use c for the constant of integration.) [ (41²³1 (4t³i + 14tj - 6√tk)…

A: Given that we need to solve the indefinite integral with using integral constant C.

Q: (D²+1)y= tan x

A:

Q: tutor

A:

Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

A:

Q: Homework 12 Polar: Problem 6 Find the area enclosed by one loop of the lemniscate with equation ² =…

A:

Q: Find the first four nonzero terms of the Taylor series about 0 for the function f(x) = √1+x cos(3x).…

A: We need to find polynomial series.

Q: Solve the initial value problem. Y 6 dy dx 2xy = 8x, y(0) = 5

A:

Q: interval of convergence = 0

A: Follow the procedure given below.

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

A:

Q: Sketch the region enclosed by the curves and find its area. y = x, y = 3x, y = -x + 4

A: Given; y=x, y=3x, y=-x+4   Now find the point of intersection between the line y=-x+4 & y=3x.…

Q: Differentiate: arcsin (# )+ 0 1 (E) None of these O x/y O y/x 00 + arccos (-) = 1

A:

Q: Find the limit. lim (t i 6 j + t² k) t-5 lim (t i − 6 j + t² k) = i t-5 i+ i j+ i k

A:

Q: VI. Suppose f is continuous everywhere, f' is differentiable everywhere except at x = -1, and the…

A:

Q: Find r'(t), r"(t), r'(t) r"(t), and r'(t) x r"(t). ● r(t) = 2t²i - 2tj + 53³k (a) r'(t) (b) r"(t)…

A:

Q: Verify Green's Theorem by evaluating both integrals ON √ y² dx + x² ov - [/(2x - 2M) da dA R ax ду…

A:

Q: 8. Use differential to estimate the value of √ 4.01 four decimal places. 9. Use differentials to…

A: We have to find 8.The value of √4.01-1/√4.01 upto four           decimal places.  9. The value of…

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) [0, 6] x2

A:

Q: The graph y=f(x) is given; transform the graph y=f(x) into y=2f(x+1)

A: Given: Line passing through 0, 0, 4, 4:  y=x    {0≤x≤4}The equation of the curve is y=x-52+3…

Q: Find the limit. NOTE: Enter the answer using round brackets. t² +7 1 lim t +∞o (?, ?) 5t² + 6'5t,

A:

Q: yk T cross-section 30 beview The base of a certain solid is the area bounded above by the graph of y…

A: We have to find the volume.

Q: Calculate the length of the path over the given interval. (sin 7t, cos 7t), 0≤t≤n

A:

Q: Write the given (total) area as an integral. • The area above the x − axis and below y = 4 − x²

A:

Q: = The Taylor series for f(x) = √2x − x² at a : 1 is Σ Cn (x - 1)”. n=0 Find the first few…

A:

Q: .3 t +y3

A:

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A:

Q: h₂ = = 3.75 sin(736t) + 7.5 and h₂ = 3.75 sin(736(t + 4))+ +7.5

A: answer of given question is in next step

Q: and the magnitude of the given vector. (-4, 4, 7)

A:

Q: Find the area of the region between the curves y = 12 - x² and y = x² – 6. Area between curves =

A: To find the area between the given curves

Q: f(x) = 2x + 3 x 1 1 ; a = 1

A: limx→1+f(x)=limx→1+x2+2                =12+2=3limx→1+f(x)=3

Q: Find the derivative of the function by the limit process. g(t) = t³ +7t g'(t) =

A: We have to find derivative

Q: (D²4)y= 8e²x - 12

A:

Q: Find the slope of the tangent line to the polar curve r = sin(70) at 0=. Enter as an integer or…

A:

Q: Use Green's Theorem to evaluate the line integral Jo (y - x)dx + (2x - y)dy for the given path. C: x…

A:

Q: If In a 2, ln b = 3, and ln c = 5, evaluate the following: = (a) In (10-2) = b-4c² (b) In √6-³c-²a-1…

A:

Q: r(t) = (t, In(t), √t), to = 1 e the equations for the line to approximate r(to + 0.1). to + 0.1) =

A:

Q: Find the limit. Use l'Hospital's Rule wher lim [In(x⁹ – 1) – In(x³ – 1)] - - *-1*

A:

Q: Find T(t) and N(t) at the given point. r(t) = 7 cos(t)i + 7 sin(t)j; t = 3 T() = N() =

A:

Q: Use the following binomial series formula to obtain the MacLaurin series for ∞ (a) (1+z) k=0 (b) √ 1…

A:

Q: e3x-6-2, [2x - 5], √x²-9, if x ≤ 2 if 2 3

A: answer is in next step

Q: Find the indefinite integral. (Use c for the constant of integration.) [(41³i+ (4t³i + 14tj - 6√tk)…

A:

Q: Write TRUE if the statement is correct, otherwise write FALSE. THERE IS NO NEED TO JUSTIFY YOUR…

A:

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A:

Q: I need all the integrals of the trigonometric ratios

A: ∫sin x=-cos x+C∫cos x=sin x+C∫tan x =-ln|cosx|+C

Q: Given the function f(x) = -√√x + √³, find f'(6). Express your answer as a single fraction in…

A:

Q: Use Green's Theorem to evaluate the line integral. S y² dx + xy dy C: boundary of the region lying…

A:

Q: A manufacturer has determined that the total cost C of operating a factory is C = 2x² + 60x + 200,…

A: Given problem:- A manufacturer has determined that the total cost C of operating a factory is   C =…

Q: (D² - D-2)y = cos x

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

Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

A: Let's find.

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A:

Q: = ||r' (t) x r' (t)|| ||r' (t)||³ to find k(t). r(t) = 7 cos(9t)i + 7 sin(9t)j + tk Use the formula…

A: find curvature