Find the first and second derivative for the following functions. 1. y =tan(x) 2. Y = 3(x²-4)5 no retakes of the mai. 3. y= 2x+3 x-1

Q: Find the exact value of cos( O 1 V2 O √3 2 0 -13 O 12 2 큼 -9 4

A: We can find the exact value in the below steps.

Q: Evaluate the integral 0 L 6x (x²+1)³/2 dx.

A:

Q: 4- Say whether each given sequence is a geometric sequence, or not. Find the common ratio and the…

A:

Q: Find the quadratic function f(x) = ax² +bx+c that goes through (3,0) and has a local maximum at…

A: Given that a quadretic function f(x)=ax2+bx+c that goes thorugh (3,0) and has a local maximum at…

Q: 4 Suppose that f(x, y) = 2x² + 2y¹ − 1xy Then the minimum is

A:

Q: Solve by separation of variables: dy dx y²-4 x²-1

A: According to our guideline we are supposed to do the only first question if you want any particular…

Q: -X 17) y=e^· cos(2x); dy = ? -X A) -ex (cos 2x + 2sın 2x) B) e (sin 2x- ccs 2x) c) 2ex Sin (2x) -X…

A: Given:- y=e-xcos2x

Q: Topic: Maxima-minima/optimization problems: Inverse trigonometric Functions For example, suppose we…

A: Minimum value= -pi/2  Maximum value = pi/2  For detail...go through the solution

Q: Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of…

A:

Q: 31. dy If x³ - 2xy + 2y³ = 4 then, in terms of x and y, dx

A:

Q: Find f sin ¹xdx -

A: Given query is to find the integral.

Q: (th) h B) none existent 2) lem Cos ho A) | TheR c) 0 D)(-1) E) None

A:

Q: Use Right-endpoint Rule with n = 5 to approximate ²x x√x+2dx to 4 decimal places.

A: INTRODUCTION:  The height of the approximating rectangle is calculated using the right endpoint of a…

Q: Find the value of a that makes the following function differentiable for all values of x. g(x)= ax…

A: According to question, Given Function,gx = axif x<0x2-7xif x≥0

Q: Determine the general solution of the DE y (4) + 3y – 4y = Ⓒy=c₁e*cosx+c₂e y=ce*cosx+c,e=*sinx -X -X…

A: given   y(4)+3y''-4yput  d=d dx(d4+3d2-4)y=0for auxilary reuation put d=m and y=1

Q: An airplane flies at an altitude of a = 6 miles towards a point directly over an observer. Consider…

A: According to question,Given data,a = 6 miles,x = 10 miles,Speed of the plane = 400 miles per hour.

Q: (D7 + 2D6 + 7D5 + 14D4 + 8D³ + 16D² - 16D - 32) y = 0

A: The given differential equation D2+2D6+7D5+14D4+8D3+16D2-16D-32y=0. We have to find the general…

Q: 5) ftan5 x sec^x dx = tan6x 6 a) b) tan x 8 tan'x 7 + + tan 5x 5 + + c + c sec7x secx c) 7 5 d) None…

A: To evaluate the following integral.∫tan5x sec4x dx

Q: Topic: Maxima-minima/optimization problems: Inverse trigonometric Functions Find the maximum and…

A:

Q: Evaluate sin 5x cos 4x dx

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Differentiate the function. g'(x) = g(x) 에너 1 VX +x

A: Given:g(x)=1x+x5

Q: Identify the coordinates of any local and absolute extreme points and inflection points. Graph the…

A:

Q: assume that Dr. Kim decides to purchase a car which is selling for $55,000 today. She needs to make…

A: Given query is to find monthly payment.

Q: Find the exact value of cot-¹(-3) O O O O TU 6 0 H|6 TU 픔

A:

Q: Two sides of a triangle are 16 and 8. Find the size of the angle 0 (in radians) formed by the sides…

A:

Q: A football Jersey is marked Jown 13 dollars each week for 4 weeks. Find the total change in the…

A:

Q: Differentiate the function. f'(x) = f(x) = sin(7 In(x))

A: Given,           fx=sin7 lnxTo find : Differentiate the function.

Q: bounded by the following curves: y = x³/2, y = 8, x = 0, y = 0. Find the volume of the solid…

A: Given ,       y = x32 ,  y=8  ,  x= 0 , y=0.  From Shell method-     Since the revolution is around…

Q: Find the Laplace transform of f(t)=sin(2t) + cos (21)

A: we know  Lsin(kt)=ks2+k2Lcos(kt)=ss2+k2given  f(t)=sin(2t)+cos(2t)

Q: 4) f(x²+2) lnx dx = a) (+x) Inx--x+c b) (+2x) inx--2x+c c) (x² + 2) lnx--2x+c d) None of the above

A:

Q: (-26)³ 6 If so, write it in the form f(x) = kx². Is the function g(x) The function is g(x) = kx² ||…

A:

Q: What is the Remainder R, when ƒ(x) = is divided by (x + 1)? 20 16 22 30 30 4x³ + x² - 3x + 2 3 =…

A: To find the remainder

Q: 16. If h(x) = f(2t +Vt) dt, find h'(-2).

A: If hx=∫0x32t+t3 dt, then to find h'-2.

Q: Referring to the graph of f shown, use the graph to determine the value of the definite integral. S…

A:

Q: Find the limit (if it exists). lim f(x), where f(x)= x+1- [x³ +2₁ x < 1 x+2, x ≥ 1

A:

Q: Determine the solution of the following differential equations. a) (D² +9) y = 81x² + 14cos3x

A:

Q: The measurements of the base and altitude of a triangle are found to be 46 and 34 centimeters. The…

A: Given information altitude ( A ) = 34 cm Base ( B ) = 46 cm let Area = A

Q: (b) (i) Fill in the missing parts: The Ratio Test for (ii) Find the value of L. Σ gives L = lim n=0…

A: To use the ratio test

Q: Find the general solution of the D.E. (4D³ − 3D+1)y=0. Ⓒy=c₁e²x+c₁₂e-²x Ⓒy=c₁₂e-*+c₂e² Ⓒy=c₁e²+c₁₂e…

A:

Q: (9)- ८ X+3 tran(x) d. y = √x ln (x)

A:

Q: 4. Using a right triangle, find the exact value of cos cos (tan-¹²).

A:

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A: use derivative and critical points for absolute maxima/absolute minima

Q: 1) The derivative of y = esec-12x, x > 0 is: a) 2e³ec-¹2x x√4x²-1 esec-12x b) x√4x²-1 C) x√16x²-1 d)…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Consider the function f(x, t) = x³e-, where c is a constant. Find the indicated partial derivatives,…

A:

Q: Find the exact area of the surface x = 6t - 2t³, y = 6t², obtained by rotating the given curve about…

A:

Q: Use the summation formulas to rewrite the expression O O 4 8 71 72 6 8 6 S I I I + n 8 4 72 8 S…

A: 12+22+...+n2 = n(n+1)(2n+1)6. 1+2+...+n = n(n+1)2

Q: Determine the slant asymptote of the graph of f(x)= x²-8x+14 x-3 Write your answer in the format y =…

A:

Q: How long will it take for the population to reach 80738073 deer, according to this model?

A: Given that, the population of the deer grows as per the given model:     Pt=2993t2     , where t…

Q: 11. Determine f'(x) for the function f(x) = 5e4-9. Show your work. a. f'(x) = -25e4x-93 b. f'(x) =…

A:

Q: Use the Fundamental Theorem of Calculus to evaluate by hand using antider- rivatives. Show all work.…

A: