Assume a particle’s position is given by f (t) = −4 / t, where t is measured in seconds and f (t) is given in centimeters. What is the velocity of the particle when t = 1?

Q: ind the derivative of the function f(z) = (2r+7) 71+11 %3|

A:

Q: 1. Write the equation of the line tangent to f (x) =1 + e*sin(2x) when x = 0. %3D %3D

A:

Q: Describe the change in accuracy of dz as an approximation of ∆z as ∆x and ∆y increase.

A: Given , z=fx,yWe do dz using the partial derivates zx & zy .So , dz=zx.dx & zy.dywhere zx…

Q: The equation of the tangent line to f(x) = 5x2 + 7 at x = 0 is a y = 5x + 7 b y = 7 y = 2x + 14 O d…

A:

Q: For f(x)=x5, the instantaneous rate of change is known to be 405 at x=-3. Find the equation of the…

A: y=fx=x5instantaneous have of change is known to be 405 ,or x = -3∴ y=f-3=-35=-243

Q: 8 S(x)= Vx? +6x at x = 2

A:

Q: 2 5. x=- 1+t2 2 y=, t(1+t?)

A: Given: x=21+t2, y=2t(1+t2).

Q: for the function f(x) = 2 cos(45x)o , determine: the instantaneous rate of change at x = 12. you…

A:

Q: Find the equation of the tangent line at x = 2 for f(x) = 4+x-2x²-3x³. Write the answer in the form…

A:

Q: Find an equation of the line tangent to the curve y = e at (0,1). 2x

A: We need to find the equation of tangent to the curve: y=e2x  at (0, 1) This can be done as follows:

Q: Find the equation of the tangent line to f-l x+4 at the point P (,0) for f(x) = 3x + 3

A: f(x)=(x+4)(3x+3)=x+13(x+1)+33(x+1)=13+1x+1 f'(x)=-1(x+1)2 f''(x)=2(x+1)3 the slope of the tangent at…

Q: Find the equation of the tangent line to the function f(x)=2x^2−9 at the point where x=−6. Give your…

A: Calculate the derivative of the function at given point than write the equation of tangent line.

Q: The function f(x) = 1 + x decreases to 1 as x- 0. Does f(x) dx exist?

A: Given function is f(x)=1+x-1f(x)=1+1x Given integral is evaluated as follows.…

Q: B] Find the equation of tangent to y = 100e-U. -0.1a when x = 0. ||

A:

Q: Find f (3) and f' (3), assuming that the tangent line to y = f (x) at a = 3 has equation y = 5x + 2.

A: Tangent to a function at a point is a line which just touches the graph of the function at that…

Q: 3. For the fiunction g(x) = x - 2x² –1, at what tangent point(s) is the instantaneous rate of change…

A: given function :

Q: What is the equation of the tangent line to y=e^7x−9/e^x at x=0? Write the equation in…

A:

Q: Let f(x) = 3x^2 + x + 5. a) Find the equation of the tangent line at x = 10. b) For what value of x…

A:

Q: At the point where x = 0, the tangent to f(x) =e* +px+q has equation y = 5x-7. Find p and q. %3D

A: slope of tangent to curve f(x) is f'(x)

Q: (b) What is the equation of the tangent line for f(x) = x² – 1 at r = 4?

A: f(x) =x2-1

Q: (b) Use your answer from part (a) to evaluate the derivative. (ӕ — 5)30 In d dx V (2а — 7)34 -

A: first, simplify the function ddxlnx-5302x-734 =ddxlnx-5302x-73412 =ddxlnx-53022x-7342…

Q: Find f(3) and f'(3), assuming that the tangent line to y = f(x) at a = 3 has equation y = 5x +2.

A: Consider the provided function, y=5x+2 Find the value of f3  and  f'3 at a=3. y=5x+2 We can write…

Q: The rate of change of y is proportional to y. When t = 0, y = 2, and when t = 2, y = 4. What is the…

A: Given that rate of change of y is proportional to y that is, dydt=ky        ...(1)

Q: 2) Find the equation of the tangent to f(z) = 3re² when x = 1

A: A detailed solution is given below.

Q: Find the equation of the tangent line to the function f(x)=2x2-x  at the point where x=−1. Give your…

A:

Q: Find the second derivative f"(x) for f(r) = e(z+2)*.

A: Given: fx=ex+24 for finding second derivative of given function we first take log and find first…

Q: Find the equation of the tangent line to f at x = a. f (x) = 3 − 4x,             a = 2

A:

Q: Find the equation of the tangent line to y = e-9* at t = 0. y =

A:

Q: Find the 127th derivative of (1 t a*) 16 at r 0.

A: we need to find 127 derivative of given f(x) so we need to apply product rule

Q: What is the slope of the tangent line that touches the graph of In y + e2"- = 3y – 4r at the point…

A:

Q: 8. For the function f(x) = x2 - 2, find: a) The slope of a tangent line at x = a.

A: To find the slope of tangent line at x=a.

Q: e. Find the equation of tangent line to the cubic x³+ 6x² + 10x + 8 parallel to the l y = x .

A:

Q: Find the slope of the line tangent to the curve x^3 - 3xy + 4x = 2 at x=1.

A:

Q: Find the equation of the tangent line to the function f(x)=x3+3x2+x+4 at the point where x=−2. Give…

A: we have to find tangent line at x=-2given

Q: Find the slope of the tangent to Ax) = x²e* at the point (1, e). a) e b) 1 c) 3e d) 2 + e

A:

Q: Find the equation of the tangent line to the function f(x)=−4x2−3x+2 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1given

Q: Find the equation of the tangent line to the function f(x)=−3x3−2x2−1 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1

Q: How do u solve for x assuming the lines which appear tangent are tangent?

A: Use angle formed by two tangents formula

Q: for f(x, y) = sin(O 2- Find the third derivative for

A:

Q: B) Find the slope of the line tangent to the curve y = sin x at the point where x =

A:

Q: Find the first derivative j 27 (x+2)³(2x+7y)² (y is a constant)

A:

Q: Find the equation of the line tangent to f(x)=3/(2x+1)at the point (1, f(1))

A: Given function is  fx=32x+1

Q: 2 2х + 2х +1 G(x) = Jsech(x) y e dy

A:

Q: Find the slope of the line tangent to the curve y =x-2x+ 1 at x 1 01 O 1/2 O 1/3 O 1/4

A:

Q: B) Find the slope of the line tangent to the curve y = sin3x at the point where x =

A:

Q: Find the derivative. S² 5x 39) y = At dt

A:

Q: Use forward-difference formula to evaluate the first derivative of y = x² + 4x – 5 at a = 0 using a…

A: The forward difference formula is : f'(x)=f(x+h)-f(x)hWe have to find the first derivative of…