Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle. π/8 sin П Cos T tan 8 800 = = 11 √2-1 2√2 √2 +1 2√2 √2-1 √2 +1

Q: 3) Find y' if y= e ²x

A:

Q: A hot-air balloon is held at a constant altitude by two ropes that are anchored on the ground. One…

A:

Q: Let y=5x. Find the change in y, Δy when x=1 and Δx=0.4   Find the differential dy when x=1 and…

A:

Q: Question 7. Express lim [sin² (3+3)+2 (3+³)] / as a definite integral of a function nxi=1 from x=3…

A: The solution is shown in step-2

Q: Find A. A = (4A)−¹ = || 28 [²8] =

A:

Q: 1. Evaluate the trigonometric limit if it exists. Express your answer interms of the real numbers a,…

A:

Q: Consider the rational function g(x) 3x²-5x-2 (i) Factorise the numerator and denominator. (ii) Find…

A:

Q: 3. Evaluate the limit if it exists. If the limit does not exist, answer with either +∞, -∞ or DNE.…

A: Using the bounded ness of sin function As per our guideline we supposed to answer only first…

Q: y = ln (x+1) 2000 (sinx) 300 (3x+2)"

A: we have given function

Q: -Find the surface area obtained by revolving y = sin x over [0, π] about the y−axis. Sketch.

A:

Q: Use one of the formulas below to find the area under one arch of the cycloid x = t - sin(t), y = 1 -…

A:

Q: 5 Calculate XkYk for the n = 5 data points (X₁,Y₁ ) = (2,4), (×2,V₂) = (3,5), (X3,Y3) =(4,8),…

A:

Q: Find the equation of the tangent to the curve y = ln(√x) at x = e. y=In(√x) at x = e.

A:

Q: The following triangle depicts the case of the Law of Sines (AAS). 40⁰ B O True 22.5° O False

A:

Q: 31. If f(x)=x+for all x = -1, then f'(4) =

A:

Q: exact value of cos²() using a suitable power-reducing formula. + √2 4 1-√2 2 1+√2 2 2-√2 4

A:

Q: Determine which set of vectors is not orthogonal. n tonight F1 ! O V = 5i; w = 2i v=8i +4j; w=i-2j…

A:

Q: Which of the following properties of vectors is incorrect? à × b = b × ā X à · ( b + c ) = à · b ± à…

A: The vectors are  and

Q: a) Use the binomial series to give the first 3 non-zero terms of the power series for 1 +... √1-4x2…

A:

Q: Use implicit differentiation to find an equation of tangent line to the curve sin x + cos y = 1 at…

A: The equation of the curve is given that is,

Q: Determine whether or not the vector field is conservative. If it is conservative, find a function f…

A: We have to determine whether or not the vector field is conservative. If it is conservative, find a…

Q: Write v as a linear combination of u₁, 2, and u3, if possible. (If not possible, ente v = (7, -9,…

A:

Q: Ifv=i+2j and w = 3i+ 6j, then the projection of v onto w is: O 1i - 2j O i + 2j O O -3i - 6j 3i+ 6j

A:

Q: 10. A stone is thrown vertically upward from the ground with an initial velocity of 128 ft/s. Find:…

A:

Q: 4 (6) Find the derivative y' for the Following function 2x 1) Y = √₂²² sin (e²-1)dt 2y=1-cos (x ²-2)…

A:

Q: If x² + y² = 4, then 0-12/0 00 04-4 0- - O 1. 13. de =

A:

Q: Determine the intersection of the two planes: ¹₁:3x + 2y - 6z - 5 = 0 л₂: 2x + 3y9z+10=0

A: We have two equations 3x+2y-6z-5=0 2x+3y-9z+10=0

Q: Rationalize the following denominator: √5-3√3 √6 3√10-6√2 6 O√30-6√2 3 3√10+3√2 6 √30+9√2 6

A:

Q: 8) Evaluate So (x-1) dx Dod

A:

Q: 5. Determine the equation of the curve whose tangent line at any point (x,y) is e* — sin x and…

A: Determine the equation of the curve whose tangent line at any point (x, y) is ex – sin x and passes…

Q: The slope of the tangent line to the curve ln(cy) = z² at the point (1, e) is 0 00 Ove Oe-¹

A:

Q: If two vectors are True orthogonal, then their dot product is -1. False

A: given statement is if two vectors are orthogonal, than their dot product is -1

Q: Evaluate Given Limits a. Lim (6h+h²+3) →>0 b. Limo 4h+h² 4 c. Lim (1+2h+h² +2+2h) d. Limo 2xh+h²-2h…

A:

Q: SC y Jo Jo (xy + 1) dy

A: The given integral is:

Q: Determine the derivative for y ду = ?х ду ?х ду ?х ду ?х 5 cos (2x-4) = = 5 sin (2x - 4) = 10 cos…

A:

Q: Find dy dx at the point (0, 2) if y² +e™ = 4.

A:

Q: The graph below is the derivative, f'(x), of the continuous function f(x). -8 -4 -3 -2 6 -5- 4 -3 2…

A:

Q: Let f(x) = 4x²-x² c) find f"(x), the intervals on which F(X) is concave upward, the intervals on…

A:

Q: Find an equation in cylindrical coordinates for the rectangular equation Entry Tip #1: To enter ,…

A: We have to find cylindrical equation of the the rectangular equation

Q: Find the vector that is orthogonal to the projection vector that comprises the sum of two vector…

A: Given: v=-i+2j and w=3i-j

Q: 5. lim (5x³ - x²y²) (x, y)-(1,2)

A: You have specifically asked to solve question number 5. So, we will solve Question number 5 for…

Q: Use the Intermediate Value Theorem to show that the equ (77) = ecos(7 (0.1) sin

A:

Q: (a) x® (d) 2x7 ex (b) e¹ (c) x² √√x³ (e) x+1

A:

Q: Q4: Solve the D.E x²y" - 2xy' + 2y = x²

A:

Q: If two vectors are O True orthogonal, then their dot product is 0. False

A:

Q: I = [₁²₁ √√√t-1d y = 1≤x≤ 16

A:

Q: Use the following function and its graph to answer parts (a) through (d) below. Let f(x) = 5-x, x3.…

A:

Q: Determine the solution to the following system of equations: (3) 1 HUNGA 11 ++ I 1-63-62-6 b b b ++…

A: First we eliminate z from this system of equations.

Q: If f(x) = eV/2, then f-¹ (2) is O3 log2 ○ 2(lnx)³ ○ 3(In x)² O the inverse does not exist O2 logg

A:

Q: Evaluate the following double integral. J₁ 2² ²+1 ¹² - dA, D = {(x, y)|0 ≤ x ≤ 4,0 ≤ y ≤ √T}.

A: