Find the equation of the tangent line to right branch of the hyperbola π π ㅠ x = sect, y = tant, st≤ 12 at the point (√2, 1) where t = 2 4

Q: 4. Find an equation of the tangent line to the curve, f(x) definition of the derivative. (Don't use…

A: Given problem:- Find an equation of the tangent line to the curve, f(x) = 1/(x2 + 1) by using the…

Q: Evaluate the double integral: 2 So de dy. Sola 0 Jy¹/3 Y x7 +1 (Hint: Change the order of…

A: Application of integration

Q: find the solution of the problem with given initial value, using homogeneous equations with constant…

A:

Q: 2. Find the horizontal asymptotes of the following functions. 9x2 + 1+ 2x + 1 (a) f(x)= = 4x + 3

A:

Q: Fill in the blank. (Note: The notation x→ c' indicates that x approaches c from the right and x → C…

A:

Q: 4. find the given general differential solution, using homogeneous equations with constant…

A:

Q: 4 Use technology to help you sketch the graph of each function for 0 ≤ x ≤ 27. a y=sin x by=sin 2x…

A:

Q: The illustration below shows the graph of y as a function of x. Determine the kind of function…

A: Explanation of the answer is as follows

Q: tan²7x dx

A: SOLUTION-

Q: Farklı yaklaşım doğrultuları kullanarak aşağıdaki fonksiyonların (x,y) (0, 0) için limitinin…

A: Find the limit for (x,y)=0,0   using different wayslim x,  y→0,  0x4-y2x4+y2

Q: Find the area of the triangle below. Carry your intermediate computations to at least four decimal…

A: Given.

Q: 2cos^2(?) sin3? dx

A:

Q: Find the values of x for which the function is continuous. -6x + 5 if x O x # 0 O x # 5

A:

Q: Let f(x) be a function which has inverse. If f(3)=8 then f-1(8) equals a. 8 b. -5 c. 5 d. 3

A: It is given that,  f(3)=8 f-1(8)=?

Q: 4. Evaluate the double integral: L Lates y¹/3 x² 27 +1 (Hint: Change the order of integration to dy…

A:

Q: Consider the substitution 1 u(x) y(x)* What is ? Use the substitution to obtain a 1st-order linear…

A: Explanation of the answer is as follows

Q: 4. Find the equation/s of the normal line of slope 2 to the ellipse x² + 2y² = 3. 5. At what point…

A:

Q: Q1/ evaluate. SPS dj dz dx X+2

A:

Q: Find two positive real numbers such that the sum of the first number squared and the second number…

A: Convert it in one variable then use double derivative test

Q: Use mathematical induction to prove the following: 1 + 3 + 5 + ... + (2n – 1) = n² for n ≥ 1

A: This question can be solved using the four basic steps of mathematical induction.

Q: Find the dimensions of a rectangle with area 2,197 m2 whose perimeter is as small as possible. (If…

A: Let's find Dimension of rectangle.

Q: find the solution of the differential equation     dy / dx = y / (y-x)  with y(5) = 2

A:

Q: S. (2w² - 5w+3) dw 4. S. (36+4) ² db 1 v dv S. 6. v² 7. J. ze³z²-1 dz 8. S.2²2 ydy 5. e

A:

Q: 15.) X (2x+5) 2 dx

A: Indefinite integral

Q: sin4 x cos5 x dx

A: To solve: The integral ∫ sin4xcos5x dx Formula used: cos2x=1-sin2x Power rule of integration:…

Q: 4. Letf(x)=x22/5 - 19x². Determine the largest n for which fis n-times continuously differentiable.

A:

Q: T (3 sec² x + 4 csc² x) dx 3

A: The given integral,        ∫π3π43sec2x+4csc2xdx

Q: (6) _ z² = pqxy

A:

Q: What is the 100th term of the sequence –3, 2, 7, 12, ...?

A:

Q: Find the value of t(5) if you are give t(3)=-1 and the non-recursive formula is given as…

A:

Q: Determine whether the given function is even, or odd, or neither. One period is defined for the…

A: We have to find if the function is even or odd.

Q: 3. Set-up the iterated double integral in polar coordinates that gives the volume of the solid…

A:

Q: H.W: Evaluate the integral 30 1. [[(x²y = 2xy)dydx 0 (2x- - y)dydx 2m [[(sinx+cosy)dxdy 3. 5. 2. (x…

A: Since you have posted a question with multiple sub parts, we will solve the first three subparts for…

Q: Qs/ Find the ave of the region R enclosed by the parabola x = - y²) and the line Y. X +2

A: find the shaded area

Q: Evaluate h(4), where h = go f. 3 f(x)=√x²9, g(x) = 6x³ +9 h(4) =

A: The given functions,fx=x2-93, g(x)=6x3+9

Q: xe. xe2x dx

A:

Q: Using mathematical induction, prove that 1²+2²+3²+ ... +n² = for all positive integers > n(n+1)…

A:

Q: Q4) Find the volume of the region R, that cut from the cylinder x² + y² = 4, by planes: z = 0 and…

A:

Q: Show that the equation is homogeneous and find its solution. dy/dx=x+y/x

A:

Q: The demand function for a firm's product is given by q = 18(3p, 2p)¹/3, where • q = monthly demand…

A:

Q: What is the general formula for the nth term of the sequence –4, 1, 8, 17, 28, ...?

A: To determine the general formula for the nth term of the following sequence.  –4, 1, 8, 17, 28, ...…

Q: 1 (2m-3)√4m (m-3) dm

A: Given

Q: A student is given four different trigonometric expressions 1 I secx cosx 9 II cot²x-csc² x III…

A: Let's simplify given trigonometric function and then evaluate for ranking.

Q: IV. Evaluate: lim (x² + €¯²) (² - ¹ cs

A: We can evaluate the given limit by using the properties of  limits.

Q: Given g(x) = -10x-2 -5x-2' Provide your answer below: g'(x) = find g'(x) using the definition of a…

A:

Q: Consider the function f(x)=2 sin (4(x-3)) +6. State the amplitude A, period P, and midline. State…

A: Given:       fx= 2 sinπ4x-3+6

Q: A- L [ Sin2t + cos2+] ² 2 B 32 3-2 [37-² + cost's *] 3 2

A:

Q: The graph shown is f(x) = 1⁄x². Y 5 4+ 3 2+ 1 + 54 3-2-11 1 2 3 4 5 -2 -3- 4 -5 X If g(x) = f* f(t)…

A:

Q: IV. Evaluate: lim (x² + €¯²)(x-¹ csc csc z) z→0+

A: Given :limx→0+x2+e-xx-1cscx

Q: H.W find the first four terms of the binomial series for the functions:- 1-(1-x)-¹2 2-(1+)-²…

A: As per the guidelines I am supposed to do the first question among multiple questions. So here I am…