7. Let D be the region between the curve y= f(x) >0 and the x- axis on the interval [a,b],x e[a,b], then S(D) =, 8. [IS(x) ±g(x)]dx =, S'kf(x)dx =. (k is any cons tan t) 9. Newton-Leibniz formula (the fundamental formula of calculus)

Q: 6) Find all relative extrema in the function h(x)=cos on the interval [0, 2].

A: For any function f(x) which is defined over an interval [a,b], its relative extrema values are the…

Q: 7. Use calculus to find the exact values of the x-coordinates of all points of the graph of f(x) =…

A:

Q: (a) f(x) = F(x, 2): then ƒ'(x) = (b) f(x) = F(4,x): then f'(x) = (c) ƒ(x) = F(x,x): then ƒ'(x) = (d)…

A: Total derivative of function z = f(x, y) is given as dz=∂z∂xdx+∂z∂ydy We are allow to solve first 3…

Q: The acceleration of a particle is defined by the relation a = A – 6f, where A is a constant. At t =…

A:

Q: sir(*) F(x) = ["cos (?' )at # 26 If find F'(x). (A) cos(x) cos (sin'(x)) (B) cos (sin'(x) }in(x) cos…

A: Leibnitz Rule of differentiation:       ddx ∫α(x)β(x) f(x,t) dt =∫α(x)β(x) d(f(x,t))dx dt +d(β(x))dx…

Q: Pr. #1) Find the exact value of So f(x)dx using the graph of f below.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: lim tanx i. x→ 0 lim In(1+ x)] 11. x→ 0 lim sin ax i1. where a and b are constants. r0sinbxr

A: We are only allow to to do first question and three subpart of question So if you need rest of…

Q: E Let C₁ be the curve parameterized by r(t) = (cos² t, sint) where t = [-]. Let C₂ be the line…

A: Given that C1 is the curve parameterized by r(t)=(cos2⁡t,sin⁡t),t∈[−π2,π2].Let C2 be the line…

Q: 4. Determine all possible functions f(x) that satisfy the given conditions. (a) f'(x) = V¤ – 3 x2…

A:

Q: FIND THE DERIVATIVE OF THE GIVEN 4.) f(x) = sec x ニ 5.) y= In「3-2メ |- 3x 6.) y= Inle-*+ xe-*)

A: 4. To find: The derivative of the function. Given: The function is secx. Calculation: Use the chain…

Q: 16. Let f(x) be a differentiable function defined on [0, 2] such that f (x) = f (2 - x) for all x e…

A:

Q: Let f(2)= iz³ + cos(z²) z² +1 i. Find f'(z). ii. Evaluate ƒ'(–2i) and simplify. iii. State the…

A:

Q: 6. Let f(x,y) = sin(x + y) + arcsin (xy) a. Find the linearization L(x,y) at the point (0, ")

A: We have to find linearization of given function f(x,y): Concept: The linearization of a function…

Q: 33. T Slope of tangent line Given the function f(x) = 1 - cos x and the points A(π/2, f(π/2)), B(π/2…

A: The slope between two points of a line (x1,y1) and (x2,y2) is given by the equation;…

Q: Q.13.a) s dx x2+2x+1 b) Sx sinvx dx dx c) J Tx+V% 1E / E

A:

Q: 3. (a) Let f(t) = t – sin t for all t. Show that f is a strictly increasing function of t, and…

A: f(t) = t - sint for all t  So, f'(t) = 1 - cost for all t  &, f"(t) = sint for all t

Q: Let f be a function with first derivative given by f' (x) = r(x –5)? (x + 1). At what values of z…

A:

Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

A:

Q: y), the harmonic conjugate of u. Form the

A: A function u (x, y) is said to be a harmonic function if u _x x + u_ y y = 0.

Q: 8. (a) Sketch the graph of f'(x) by using the given graph of y = = f(x). I ¦ f(xX ¦ 11 r-x--r 14

A:

Q: 1. ('88 BC) The length of the curve y = x³ from x = 0 to x=2 is given by 2 2 A) [√₁ + x ²dx (B) √ √…

A: Given,.Formula for length of the curve is,

Q: Prove: If α∊R, then the function αf is differentiable at c, and (αf)'(c)=αf'(c)

A: