6. A model for the length of daylight (in hours) in Philadelphia on the t day of the year is given by: 2л L(t) = 12 +2.8 sin (365 (-80) Use this model to compare the rate of change in daylight in Philadelphia on March 21, the 80th day, and May 21", the 141" day.

Q: Suppose thnat the tangent line to the graph or J is equal to the tangent line to e graph of g(r) =…

A:

Q: 1. Find the slope of the tangent line at the indicated value for each function. Show all process…

A: Differentiate the given function with respect to x and then put the given value of x in the…

Q: Let θ (in radians) be an acute angle in a right triangle and let x and y, respectively, be the…

A:

Q: , Suppose that the tangent line to the graph of f(x) = xlb) at r = 1 is equal to the tangent line to…

A:

Q: 10. Find the derivative of y = cos /sin(tan 7x)

A: We will find the derivative using Chain rule

Q: 4) fip by implicit differentiation, where Find dr y + x?y³ = x* + y.

A:

Q: +0.0001) – 1, tan(4 4. Which derivative is approximated by 0.0001

A:

Q: 8. Find the principal value of Arc tanh(1 + j2)

A:

Q: Let θ (in radians) be an acute angle in a right triangle and let x and y, respectively, be the…

A: We have given For x = 4 units, x’ = 6 units/s and for y = 5 units, y’ = -1/5 units/s.

Q: 2. A particle moves along the parabola y = x in the first quadrant in such a way that its…

A: Given: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x -…

Q: L(cos(at)sinh(at))

A:

Q: find an equation of the tangent line at the point indicated. y = log2(1 + 4x−1), x = 4

A: We have to find an equation of the tangent line at the point indicated. the given function is…

Q: of the tangent line to the sine function at the origin. y y= sin(7 x) values with the number of…

A:

Q: 4. Find the derivative of g(x) = e5" sin(-x). Do not simplify.

A:

Q: a- y= (cosx) (use logarithm differential)

A: To find dy/dx

Q: find the second derivative and simplify the final result 7. y= Arccos(e^2x)

A: To find     d2arccos(e2x)dx2

Q: 83. Find the 50th derivative of y = cos 2x.

A:

Q: One side of a right triangle is 150 m long and its adjacent angle is t/3 radians, with t/60 radians…

A: Use derivative

Q: 20. Evaluate the derivative. 4 (sinh ) dx O

A: ddxsinh-1ex

Q: 5. If cosh 2x then the positive value of 4 sinh 2r is

A: Here we will use the relationship betweencosh2x and sinh2x to find the value of sinh2x from the…

Q: Find the surface area of revolution of 7 cos(5θ ) between - π/10 and  π/10, about the x-axis using…

A:

Q: 4. Find the derivative of the following function. 1+ sinx g(x) = - V1+ cos x

A: Given: gx=1+sinx1+cosx for finding derivative of given function, first we simplify given expression…

Q: S Sin 5t-205 2t-2(03 2€ ; s(登)=

A:

Q: VI. Determine the instantaneous rate of change of the functio: sin (³) f(x) = V² siz r³ 1 + √t at x…

A:

Q: Let 7=sin ( y+. *). Find the rate of change of z with respect to x at the point (2, 1) with y held…

A:

Q: What is the derivative of: y = ln ln(1 − cos x)

A:

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional te…

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

Q: 1 3), sinh(x)-cosh(x) dx

A:

Q: Explain graphically why there is no solution to cosh x = sinh x

A: cosh x = sinh x. We need to explain graphically why there is no solution to the given equation.

Q: Find the derivative of y = csc¯(In sin (x))

A: use simple integration formula.

Q: 1. Use the fact that coshx = (e* + e) and sinhx = 1 NIH (ex - e-*) to solve for 1 coshx+ sinhx dx

A: ∫exdx=ex+c

Q: Find the slope of the tangent line to the sine function at the origin. y 2 y=sin -1 Compare these…

A:

Q: 2. One side of a right triangle is known to be 150 cm long and the adjacent angle is measured as…

A: The given problem is to find the maximum possible error in area of triangle when one side and angle…

Q: 2. Use the identity of inverse hyperbolic function to solve cosh-(2 – a2) = ln 2, for |æ| < 1.

A:

Q: If y = 4 tanh x + sinh 2x, what is the slope of the curve when x = 2? Assume h = 0.5 and 0.01;…

A:

Q: Find the differential for y = tan 2x2

A: Find the differential equation for given equation We need to take derivative for tan using the…

Q: Use differentials to approximate the quantity   √99.7

A:

Q: If f(x) = sinh 2x − e2, find the exact numerical value of f"(ln 2).

A: Given : f(x) = sinh 2x − e2

Q: tanh 2x In (cosh 2x)dx

A:

Q: 5. Find the derivative of --( 1 + sin 0 cos 0

A:

Q: 5. Find the derivative of h(x) = cos(sin(cosx)).

A:

Q: 8. Find the derivative of the function (t)= 3sin(arccost)

A:

Q: Q2): If sinh(x) =find tanh(4x). %3D

A:

Q: 3. Find the derivative of the following function. 8(x) = cos"(vx)

A:

Q: 5. Explain in words what the output of sinh (y) geometrically represents. ule

A:

Q: Solve for the second derivative(y") of the following and simplify the final results. Show complete…

A: Given. ⇒4lntan-1x=1-y⇒y=1-4lntan-1x Taking derivative with respect to x, we get…

Q: Find the exact value of the function: 0 6 arccos (-/-)

A: See this solution in below

Q: 1. sin?(ešin*t) + cos¯'(2t³ – 5)

A: Solution: ddxsin2(esin2t)+cos-1(2t3-5)

Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLI 3x 1. Y= Arctan

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: If a stone is thrown down at 100 ft/s from a height of 1,200 feet, its height after t seconds is…

A:

Exponential Growth Model

The relation that represents an exponential function is: