Prove that the equation is an identity. 1 - sin 0 = cot 0 cos 0 sin 0 Working from the left-hand side, rewrite as a single fraction. LHS = sin 0 sin 0 1 - sin 0 Use the trigonometric identity for 1 – sin² 0. LHS = sin 0 • Cos 0 sin 0 Cos 0 Use the trigonometric identity for sin 0 sin 0 = sin 0

Q: Find the derivative of y = cos³*+8 (x). Provide your answer below: y =

A: Given query is to find the series of the expression.

Q: The regions A, B, C, and D in the figure below are bounded by the graph of the function f and the x-...

A: Given query is to find the average value of the function.

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the...

A:

Q: (3 – x if x < 2 if x 22 - 4. f(x) = { is discontinuous on the interval (- 0, 2] %3D -3

A:

Q: [3] Write the expression below as an algebraic expression in x for x > 0. cos(2 tan x) = -1

A: This question is based on trigonometric ratios.

Q: 1. What does the following numerals represent? 51651 五万六百五 Input the numbers in decimal system. Do n...

A: 1. What does the following numeral represent = 50605 The number is =  5 times 10000 plus 6 times 100...

Q: Sketch in the two level curves of: f (x, y) = y+ x² = k _for k = 1, 2.

A: Solution is written in below steps.

Q: The velocity and initial position are given. Find the position function. r(0) = (1, 2, 3) v(t) = (e3...

A: Given that, initial position function r(0) =1, 2,3  and  v(t) =e3t, sint, 6t where v(t) is the veloc...

Q: Given the differential equation In(2x – 2)dy + ydx x-1 = 0 then what is = ? 8x y y Зху? + х х-1 O A ...

A:

Q: The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=5 and x...

A:

Q: 2 5. f(x) = x3

A: We will use the definition of a derivative to solve this question.

Q: An object of mass 10 kg is released from rest 1000 m above the ground and allowed to fall under the ...

A:

Q: The position of a car traveling along a highway is given by the function s(t) = 21- 2t – 312 +6 wher...

A: I am attaching image so that you understand each and every step.

Q: T(E) = N= T'(4) Evoluate (t) NG) for t=L,

A: First we find r'(t) then put t=1

Q: Evaluate the integral. [HINT: Use a shortcut.] | 12(2x + 1)5 dx

A:

Q: the other a calculator approximation rounded to two decimal places. (a) log6(x) = -2 X = (b) In(x) =...

A:

Q: y=x and y = x3.

A:

Q: Determine whether the series is convergent orrdivergent. the exact test thhat you Use. 土2

A: ∑n=1∞ -1n1+2nn  

Q: Find the Maclaurin polynomials of orders n= 0, 1, 2, 3, and 4 and then find the nth Maclaurin polyno...

A: To find the Maclaurin polynomials of orders n=0, 1, 2, 3, and 4 and then to find the nth Maclaurin p...

Q: Do the functions y = cos5t and y, = sin5t constitute a fundamental set of solutions of the different...

A:

Q: 4 2xdx х2 — 4х + 8

A:

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w ...

A: Find your answer below 

Q: Evaluate the integral. w2 In(w) dw 1.

A:

Q: Find the derivative of h(x) = cos (2x3 - 5). %3D Provide your answer below: W(x)= O %3D

A: We will find the derivative of h(x) in the following step.

Q: Solve the following equations: (You may leave your answer in exponential form or logarithmic form). ...

A:

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of int...

A: Given problem:- Evaluate the integral using the indicated trigonometric substitution. (Use C for the...

Q: ) .3 Find the derivative of h(x) = cos (2x – 5 %3D

A: Given,            hx=cos42x3-5To find : The derivative of the given function.

Q: dy Find using implicit differentiation, for the equation + 10 is_ dx

A:

Q: y³dy Let y = 2 sin 0 %3D 4- y2

A:

Q: 2) Which of the following expressions is equal to lim (x+h)100-x100, h-0 h A) x100 B) 100x99 C) x99 ...

A:

Q: Find the length of the curve x = from y = 1 to y = 3. The length of the curve is (Type an integer or...

A:

Q: Find a differential equation whose general solution is y = cjet + cze-". = 0

A:

Q: Given the table of values below, find h'(1) if h(x) = g(x² f(x)). %3D f(x) f'(x) g(x) gʻ(x) 1 -3 -3 ...

A:

Q: Which of the following differential equations that involves differentials? ô²y ¸ ô²z d*y + 5 y dx d²...

A: In this question we have to find which differential equation involve differential.

Q: Find all the distinct cube roots of 812, then plot the results on an Argand diagrar

A: Cube root of a number

Q: Consider the following tables: -2 -1 1 2 f (x) 5 -3 4 3 -2 -1 1 g (x) 5 1 3 Fill in the blanks with ...

A: Function values of f and g are given, we have to find the following.

Q: Lind ds 6) 5. 52+w²

A: It can be solved using chain rule and divide rule of differentiation.

Q: z is jointly proportional to the square of x and the square of y. If z=364 when x=6 and y=5, find z ...

A:

Q: dy Find using implicit differentiation, for the equation æ4 + yt = 7 is dæ O O O

A:

Q: What is the general solution to the differential equation ydx - ( x - sqrt(x² + y² )dy = 0?

A: Let's find. 

Q: Suppose 2700 cm² of material is available to make a box with a square base and open top. a) Show tha...

A:

Q: In Exercises 33-36, use upper and lower sums to approximate the area of the region using the given n...

A:

Q: The total cost of producing x items is given by C(x) = 246.74 + | 3t dt- Find the fixed cost and the...

A: The given problem is solved below in detail.

Q: Evaluate the integral. 1 (x² + 3)e¯× dx 0.

A:

Q: a) logx5 32=1, then x=  b) 43x+4=18, then x=

A: Use  basic property of logarithmic function

Q: 2x + 8, z 8 is continuous at z = 8. Justify the conclusion. (i) f(8)= (ii) lim f(r)= Z-18 (iii) lim ...

A: i) f(8)=16ii)limx→8-f(x)=limx→8-(2x+8)                     =2(8)+8                                  ...

Q: Use the quotient rule to find the derivative, h' (x), of the following function. 3x h(x) = 8 - 5x

A:

Q: 5-5 18. dy dx 5-5x

A: Given that,

Q: Find the Wronskian of the functions f(t) = 5e' sin(t) and g(t) = e' cos(t). %3D NOTE: Your answer mu...

A:

Q: 3 /9ーx? 20. dy dx -3 /9ーx2

A: On solving this we will get-