If the function = (x)S x' +1 cos( 2 7x - a) if x < -1 is continuous at if x 2 - 1 x = -1 , find the value of a .

Q: The first derivative of y = cos(3x-8) is O a. - sin( 3x-8) O b. 3 sin( 3x-8) O. - 3xsin( 3x-8) O d.…

A: Given function is, y=cos3x-8.   It is differentiated as follows: dydx=ddxcos3x-8

Q: Use the product rule to differentiate the function h, where a and b are real numbers. h(x) = e¯ax…

A: According to product rule, if f(x)=u(x)*v*x) then f’(x)=u(x)*v’(x)+v(x)*u(x).

Q: Determine whether f(x)=sinx+cosx is an odd or even number

A: Given function is f(x)=sinx+ cosx

Q: Describe with a sketch the end behavior of f(x) = cos x.

A: Given:            f(x) = cos x  The cosine function oscillates between values -1, 1 as x→∞ Hence it…

Q: Find f if f"(x) = 2+ cos(x), f(0) = 2, f(t/2) = -2.

A:

Q: Let f(x) = cos(x). (a) On [0,2n) solve f(x) = 0. 4.

A:

Q: Prove the identity. Work on one side only. cos(4x) = 18 sin² x+8 sin ¹ x

A:

Q: Let f(x) 39 27 O 1 4√3 O-√6 9 3√3 .-1 (²). Then the second derivative at x = -1,f"(-1), equals = COS

A:

Q: Find f if f"(x) = 2 + cos(x), f(0) = -9, f(pi/2)=9 f(x) =

A: Solution of given question is followed by:

Q: -1 Let f(x) = tan-¹ e²². Find f" (x).

A: The solution is given below

Q: linearize the following equation to get the function f(×)=x 3 sin x + 4 cos x = e^x - 3

A: Given function is f(x)=x3sinx+4cosx=ex-3⇒f(x)=x3sinx+4cosx-ex+3=0 Let we have to linearize given…

Q: y = (cos x)* 4. Differentiate the function

A: Given :  The function  y = ( cos x ) x    To find :  The derivative of   y = ( cos x ) x

Q: If f(z)-6 tan , then find the value of f'(1) is 12 6 1 V2

A:

Q: Let h(x) = tan(3x + 7). Then n'(5) is and h'"(5) is

A:

Q: Find the derivative y = x + Vx + Vã 01+ + Ol+ + 1 1 + 쑤 None of these 3.

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: