EX-10 - Prove the following identities: a) Sin( A+B)+ Sin( A-B)= 2.SinA.CosB Sin( A+B) b) tan A+ tan B= CosA Cos SecA.Secl.CseA. CscB e) See( A+ B)- Sin 20+ Cas 20+1 CscA CscB - SecA.Sec d) -Cot e Sin 20-Cas 20 +/

Q: If f is continuous at a number, x, then f is differentiable at x. True

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Q: Evaluate the following sums using summation formulas. 10 10 10 Σ b. ) k? а. C. k=1 k=1 k=1 10 а. k=1…

A: We have to evaluate the sum

Q: The International Space Station orbits the Earth at a height of 250 miles. What is the height of the…

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Q: Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x7 1 g(x) = 5x + 1 (Express numbers in…

A: Given; f(x)=x7 and g(x)=1/(5x+1).

Q: Find the dy/dx of the parametric equations given: x= 2t² – t and y= t³ – 2t – 1

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Q: Find the length of the curve of the graph of the indicated function. y = (x + 3)3/2, between points…

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Q: Use Green Theorem to Evaluate yx'dx – x*dy where C is left half of x² + y = 25 77.7704 O 78.7712 O…

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Q: Flnd the maximum rate of change of f (x.y) =e*²+e*+2y at P (2,1) 29 e4 V 29 e 16 O 7e4 O Viet

A: gradient of function fx, y=ex2+ex+2y, at 2, 1

Q: A factory selling cell phones has a marginal cost function C(x) = 0.01? -3x + 229, where z…

A: Given problem:- A factory selling cell phones has a marginal cost function C(x) = 0.01x2 - 3x + 229…

Q: Find the area of the shaded region. r = Vcos 20 r = 9 cos 0 NOTE: Enter the exact answer. A =

A: We have to find area of shaded Region.

Q: Find the area of the region enclosed by the curves y = x² and y = x by integrating with respect to…

A: Let f(x)=y=x2      (1)g(x)=y=x          Compare x=x2x2-x=0x(x-1)=0x=0 or x-1=0x=0 or x=1Put value of…

Q: S 4x53x dx 3.)

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Q: Find the area of the region enclosed by the rose r = 18 cos 30. NOTE: Enter the exact answer. A = T

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Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating d dt dt the product directly…

A: r1(t)=cost i+sint j +3t kdr1dt=-sint i+ cost j+3 kr2(t)=2i +t kdr2dt=k

Q: Consider the following planes. 5x + 2y – z =22 X- 4y + 2z = 0 (a) Find the angle between the two…

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Q: pproximate using differentation:  e0.99 Please show step by step solution.

A: This question can be solved using the concept of approximation using derivatives.

Q: Find the limit. NOTE: Enter the answer using round brackets. t? + 4 1 lim 5t2 + 6 7t (?,?)

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Q: (8) Using Taylor's formula, e" log(1 + is approximately equal to (a) x – xy (b) х — ху + 2 (c) x +…

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Q: dz (е) dz

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Q: Find the relative maximum and minimum values. 3 3. f(x,y) =x +y° - 15xy

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Q: Evaluate the definite integral. 124 i + ej+t k dt (e" - 1) i - (e - 1) j + k o e-11-(-1)j +K i - (e…

A: see below the answer and calculation

Q: Set up the definite integral required to find the area of the region between the graph of y = y = 4x…

A: Topic:- application of integration

Q: Use any method to simplify the complex fractloh. k+1 25k 3k - 1 15k

A: Use the fraction rule; abcd=a·db·c   The given expression is: k+125k3k-115k

Q: Calculate the limit. x2 – 9 lim х-3 х2 + 5х — 24

A: limx→3x2-9x2+5x-24

Q: Find the length of the curve r(t) = t^2i − 2√2tj + (t/2 − 1)k for 0 ≤ t ≤ 1.

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Q: How can we write out the summation of this notation

A: Topic:- simplification

Q: 2. Determine whether the statement is True or False. If it is false, explain what makes it false, or…

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Q: Use Green's Theorem to evaluate the line integral. | 2xy dx + (x + y) dy C: boundary of the region…

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Q: The integral TT tan x sec?x dx O none of them is an impróper integral of type I that diverges is an…

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Q: Use the Laws of Logarithms to rewrite the expression below in a form with no logarithm of a product,…

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Q: - In an electronic device, individual circuits may serve many purposes. In some cases, the flow of…

A: Here, the given function is: p(x)=V2x(R+x)2 of power to find x that maximize the power.

Q: E-10: Let f(x) be a non-constant polynomial satisfying the relation f(x).f (y)= f(x)+f(y)+f(xy)-2,…

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Q: 2. Determine whether the statement is True or False. If it is false, explain what makes it false, or…

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Q: Using appropriate substitution xp: V9x2-36x + 37 Is equal to

A: We have to integrate given function

Q: Consider the parallelepiped with adjacent edges u = 4i + 6j + k v = i +j+ 9k w = i + 7j + 6k Find…

A: Given; u=4i+6j+k , v=i+j+9k , w=i+7j+6k Volume (V)=?

Q: Find the equation of the line perpendicular to through (7, 2) through (-1,7/2) through (1/3, 13)…

A: The line perpendicular toa) 2y-3x=1 through 7,2b) 9x+15y+6=0 through -1,72c) x+y=1 through 13,13…

Q: . The line segment from (1, –1,3) to (0, –3, 1) forms a diameter of the sphere S1. Find the…

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Q: Assume the cubic function f(z) = ar+ b +cz+d, %3D has a relative maximum value of 3 at z =-2 and a…

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Q: Find the exact arc length of the curve over the stated interval. y = 8x2/3, from x = 1 to x = 8…

A: The expression for the arc length of the curve is: L=∫x1x21+dydx2dx   Given; y=8x23x1=1 & x2=8

Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

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Q: y is a function of  x and the slope of the function is zero at x=10 then to determine that y reaches…

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Q: 17. Let y = 4t + 3, t = 6e and s = 1 + In x. Find dy in terms of x. dx %3D

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Q: Compute the derivative y dy dx y = 7x3 – x-4 (Express numbers in exact form. Use symbolic notation…

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Q: (b) A spring exerts a force of 4.2N when stretched 0.7m beyond its natural length. How far beyond…

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Q: Find the relative maximum and minimum values. f(x.y)=x +xy+y° 28y + 261

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: If g(x) J.J S. 1 -dt , find g'(2).

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Q: Define a function S: Z+ --> Z+ as follows. For each positive integer n, S(n) = the sum of the…

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Q: Consider the function f: R → R define by f(x) = a?x3 + x² with a a real constant , a + 0, We can…

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Q: A company's marginal cost function is where x is the number of units. Find the total cost of the…

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